Vectors Worksheet

The magnitude of a vector. Add vectors that are not colinear and are not perpendicular. Whether you are teaching biology, hydrology, botany, or chemistry, or just studying the lives and work of famous scientists in general, each of the following sets of science worksheets contains multiple individual reading passages for your students. Element of a matrix, row of a matrix, column of a matrix, coefficient matrix, augmented matrix, row operation, main diagonal, diagonal matrix, identity matrix, matrix addition, matrix subtraction, matrix multiplication, inverse of a matrix. Lin 2 3 One-dimensional vector addition: The result of adding two vectors is the sum (two vectors have same directions) or difference (two vectors have opposite directions) of the two lengths and the direction of the longer one. You walk 30 m south and 30 m east. Create the worksheets you need with Infinite Precalculus. The vectors CD, CA and CB are in the xy-plane (their z-coordinate is zero). Illustration of Leaning Landforms for kids - Worksheet vector art, clipart and stock vectors. 1) If the following vectors show the routes taken by the national IGCG professional alpine hiking PE hours association, find their displacement as scheduled for the Memorial Day Hike: Routes: 300ft north, 400 ft east, 500 ft south. Vectors are usually used to represent velocity and acceleration, force, and other directional quantities in physics. 1 Vectors: Geometric Approach What’s a vector? in elementary calculus and linear algebra you probably de ned vectors as a list of numbers such as ~x = (4;2;5) with special algebraic manipulations rules, but in elementary physics vectors were probably de ned as ‘quantities that have both a magnitude and a direction such as. Try before you buy. 1 Introduction: In this chapter we shall use the ideas of the plane to develop a new mathematical concept, vector. Free Precalculus Worksheets. Vectors and scalars are one of the most important chapters or concepts in Mathematics and Physics. Find the dot product of the vectors P and Q given that the angle between the two vectors is 35° and. What type of charge does a neutron have? 6. Besides the usual addition of vectors and multiplication of vectors by scalars, there are also two types of multiplication of vectors by other vectors. Scalars may or may not have units associated with them. The length represents the magnitude and the direction of that quantity is the direction in which the vector is. Vectors and Vector Algebra: Why do we bother with vector algebra? Learning vector algebra represents an important step in students' ability to solve problems. The material can be found in many places. Science Worksheets. 3 meters and Vector B is 3. Unit Overview This lesson should be presented after the students have worked with vectors in the coordinate plane. Ifyouareanindependentstudentthengood. Worksheet 2018 #1 LOWER SIX Vectors 1 1 hour This document consists of 2 pages. (b) The wind at a particular point outside. Placing the vectors end to end, the vector from the start of the first vector to the end of the second vector is the sum of the vectors. The unit vector in the direction of a given vector a r is denoted by aˆ. Two vectors of the same magnitude are added; one pointing east, one west. What is the arctangent (tan-1) of 1. The diagonal from the initial point to the opposite vertex of the parallelogram is the resultant. Sign in with your email address. Free Online Alevel, GCSE, Secondary, 11+ Maths Resources, Past Exam Papers, Worksheets, Specimen, Solution Videos, Online Test, Online Self-Assessment GCSE Vectors 2 Worksheet Book Free Consultation. We represent vectors geometrically with an arrow. Are you looking for Worksheets vectors or photos? We have 7317 free resources for you. Download on Freepik your photos, PSD, icons or vectors of Worksheets. H=10 m G=35 m F=23 m E=30 m D=25 m C=18 m B=20 mA=15 m 59° 307° 25° 224° 39° 124°. Answers on the back. Book a seat now!! twitter. We also define and give a geometric interpretation for scalar multiplication. Example: Let A and B are two vectors and C is the resultant vector. Find the dot product of the vectors P and Q given that the angle between the two vectors is 35° and. This allows you to make an unlimited number of printable math worksheets to your specifications instantly. Some of the worksheets for this concept are Vectors work pg 1 of 13 vectors, , A guide to vectors in 2 dimensions, Science 9th physics crossword name, Grade 9 department math division upper school, Vector work, Introduction to vectors, Scalar multiplication of matrices 1. You travel 25 meters east and then travel 48 meters south. 1 Introduction: In this chapter we shall use the ideas of the plane to develop a new mathematical concept, vector. Determine the magnitude (in centimeters) and direction (in standard form) of the resultant vector B – A for each of the combinations below. It can be represented by a dot product: where F is the applied force which may or may not be entirely in the same direction as s, the distance the object moves. If two vectors are added together, the resultant is found by placing the vectors to be added end to end. Vectors can be represented in component form and direction-magnitude form (They can be manipulated in standard form and. We will use all the ideas we've been building up as we've been studying vectors to be able to solve these questions. giving your answers in their simplest form. What is your total displacement? 2. Then draw lines to form a complete parallelogram. Writing vectors in this form can make working with vectors easier. The components of vector ⃗ are given as follows:. Bert pulls the box toward the. 0 km due east and then turns and flies 7. Trigonometry- Vectors SHORT ANSWER. The applet will label the two vectors and. vector when given the. This website and its content is subject to our Terms and Conditions. The pre-algebra worksheets provide simple number sentences in the form of equations with missing values, and the students fill in the answer. 19 Add and subtract vectors by their. midpoint of AB. 2 For the vectors , find the scalar resolute of. The real power in vectors resides in the ability to perform mathematical operations on them. In your textbooks, you will see vectors denoted in boldface (v), but when writing a vector, we denote it by writing an arrow above the letter (~v). Specify vectors in Cartesian or polar coordinates, and see the magnitude, angle, and components of each vector. Vectors are mathematical quantities used to represent concepts such as force or velocity which have both a magnitude and a direction. Vectors Academy. Find the dot product of the vectors P and Q given that the angle between the two vectors is 35° and. Unit 1 - Vector Kinematics. For two vectors A and B, the vector sum A+B is obtained by placing them head to tail and drawing the vector from the free tail to the free head. Express the force vector F in terms of i and j. Examples of vectors are velocity, acceleration, force, momentum etc. Download Number four tracing worksheets Vector Art. 1 m/s Y: 29. Remember that a vector is specified by its direction and magnitude, so that the two arrows of equal length pointing to the west represent the same vector, while the three arrows of equal length pointing to the north-east also represent the same vector. What is the total displacement of a trip in which a person travels 15 km [S] and then 28 km [W]? 3. The two vectors (the velocity caused by the propeller, and the velocity of the wind) result in a slightly slower ground speed heading a little East of North. ) Solution: The midpoint of the interval with endpoints ~u 2 and ~u 3 is given by ~v. Add the following vectors and draw the resultant. It also contains finding missing components from the sector using the known values. of the vector. In your helper application worksheet, you will find the vectors 1, t, t 2, and y for the U. In the coordinate plane, a vector v can be represented as an ordered pair of real numbers, v = 〈a, b〉, where a is the horizontal component of v and b is the vertical component of v. Introduction: In this lesson, vectors will be added and subtracted. For the given vectors u and v, evaluate the following expressions. Solutions of Homework Problems Vectors in Physics 12. A vector can be specified either by its magnitude and direction or by its components. Example NEWTON. 35 m/s at 57q from the x-axis. A plane is flying round trip to an destination 250 km North of its starting point. Find the direction of p 3 2 i+ p 2 j. Home > By Grade > 8th Grade Math Worksheets; The math worksheets and other resources below are listed by subject have been aligned with the 8th Grade level based on the Common Core Standards For Mathematics. Vector Algebra Assignment/Worksheet Show that the vectors If 3 2 and 2 4 4 ,a i j k b i j k c i j k= − + = − − = + − 3 2 1 are linearly independent. lesson 37 precalculus: applications of vectors - youtube. Create the worksheets you need with Infinite Precalculus. The plane flies with an airspeed of 325 km/h and the wind is blowing at 50. Calculate the (absolute value of the) area of the parallelogram determined by each of the pairs of vectors in question 21. Math 21a Vectors & The Dot Product Spring, 2009 1 Are the following better described by vectors or scalars? (a) The cost of a Super Bowl ticket. Vectors can be defined in two dimensional or three dimensional space. When adding vectors graphi-cally, put the arrows head to tail. Element of a matrix, row of a matrix, column of a matrix, coefficient matrix, augmented matrix, row operation, main diagonal, diagonal matrix, identity matrix, matrix addition, matrix subtraction, matrix multiplication, inverse of a matrix. Draw a line that gives the vertical length of this. Vectors are quite useful in simplifying problems from three-dimensional geometry. Videos, examples, solutions, activities and worksheets for studying, practice and review of precalculus, Lines and Planes, Functions and Transformation of Graphs, Polynomials, Rational Functions, Limits of a Function, Complex Numbers, Exponential Functions, Logarithmic Functions, Conic Sections, Matrices, Sequences and Series, Probability and Combinatorics, Advanced Trigonometry, Vectors and. The following is a list of worksheets and other materials related to Math 223 at the UA. Adding Perpendicular Vectors 1. Vectors in Physics: the Ultimate Convenience! Thus, you had a point, and made it into a line, and after that produced a plane, which is a simple square. Example 5: Draw the opposite velocity vector to v = 40 km/h [S63W o ] (Use 1 cm = 10 km/h) Example 6: Draw the opposite acceleration vector to a = 55 m/s 2 [115 o ] (Use 1 cm = 10 m/s 2 ). Using Vectors to Navigate (Day One), by Randall L. Vectors in Two and Three Dimensions Part 5: Vectors in Space. Since drawings can be inaccurate, an algebraic approach using a rectangular coordinate system is needed for. 2 cm/s northwest 5 cm/s west Theory: Use the same vector addition rules established in the displacement worksheet. ws#7 vectors. 1 A non-zero vector v 2Rn is called a eigenvector for T if there exists a number such that T(v) = v. Addition of vectors can be expressed by a diagram. What is your total displacement? 2. Vectors Worksheet 2; Vectors Worksheet 2 Key; Tuesday, September 24, 2019. : mass, time, temperature etc) • Educator explain and discuss with learners the following. IB MATHEMATICS SL VECTORS WORKSHEET #2 1. Home > By Grade > 8th Grade Math Worksheets; The math worksheets and other resources below are listed by subject have been aligned with the 8th Grade level based on the Common Core Standards For Mathematics. Published by Wiley. DIRECTION must be entered in degrees, increasing 'counterclockwise'. Unit vectors are vectors with a magnitude of 1. The figure below shows vector v with initial point A and terminal point B. Draw the three vectors. We offer premium technical support, an info-packed Knowledgebase, and customizable training options like online Getting Started Guides, webinars, regional classroom events, and on-site training sessions. Before attempting the questions below, you could read the study guide: The Cross Product. Mar 08, 2016 · How to cut ANY image with Cricut - How to upload your own files for cut | Cricut VS Silhouette - Duration: 15:12. Chapter 2 Test. Orthogonal Vectors Worksheet - Solutions There, are infinitely-many unit vectors that are orthogonal to b in 3-space (just choose other choices. 2 lessons of power points - the worksheet needs the vectors you want finding filling out as that didnt save properly The power points include past paper questionsLymphatic System Worksheet coloring page from Anatomy category. Vectors Worksheet - Solutions. Problem 1 : The initial and terminal points of the vector PQ are points P and Q. Add the following vectors and draw the resultant. This worksheet help you to understand how to perform vector subtraction. Worksheet 2018 #1 LOWER SIX Vectors 1 1 hour This document consists of 2 pages. Draw a sketch of the vectors (tip-to-tail), and add components algebraically. Have the students who understand how it works solve a couple examples of vector addition and subtraction problems in front of the other students. Part 2 Directions: Look carefully at the pictures below. When we need to refer to an element of a vector that is in an indexed collection of vectors, we can write (ai)j to refer to the jth entry of ai, the ith vector in our list. Calculating the magnitude of vectors is essential for all sorts of problems where forces collide. Remember that a vector is specified by its direction and magnitude, so that the two arrows of equal length pointing to the west represent the same vector, while the three arrows of equal length pointing to the north-east also represent the same vector. Linear Algebra Review By Tim K. 3 Using the same vectors as in the previous question, find: the vector resolute of. 5th Form Worksheets for Vectors and Matrices. All for the high school levels of Grade 9, Grade 10, Grade 11, and Grade 12. IB Math SL Contact  Dot Product, Parallel & Perpendicular Vectors HW: IB Question Worksheet. Do so here: Wolf One jF xj= 0 jF yj= 20 Wolf Two jF xj= 30cos30= 25. May be freely downloaded and printed for classroom use. Understand vector components. A two-page worksheet with 4 translations given in vector format. Past Paper Questions - Vectors. (a) 4 Maths Quest C Year 11 for Queensland Chapter 7 Introduction to vectors WorkSHEET 7. Using Fall Faster Gravity Worksheet, students circle what object youthink will hit the ground first by thinking about gravity’s force, acceleration, and resistance,. Suppose the position of a particle at time is given by the position vector. Ask the students: Should sailors worry about wind and current when traveling long distances. What are Scalar and Vector Quantities? Some of the quantities that we have talked about in the Forces and Motion chapter are scalars and some are vectors. Before attempting the questions below, you could read the study guide: The Cross Product. Pre-Algebra Worksheets. This worksheet help you to understand how to perform vector subtraction. Procedure A: Finding the equilibrant of two known forces. This vector addition calculator can add up to 10 vectors at once. In multivariable calculus, we will need to get accustomed to working in three dimensional space, or R 3. Basic Concepts A vector V in the plane or in space is an arrow: it is determined by its length, denoted j V and its direction. Select from 31010 printable crafts of cartoons nature animals Bible and many more. Adding and Subtracting Vectors. Vectors And Scalars. ©7 r2p0 K182k 7K 6u Xtra 0 3Swoofxt lw Ja mrKez YLpLHCx. 3 be three vectors in R2. Suppose the position of a particle at time is given by the position vector. With the Students. Worksheet 1. Vectors - length & angle between (example to try) : ExamSolutions Maths : OCR C4 June 2013 Q7(i) - youtube Video. Anything with a * next to it represents content that is brand new to GCSE Maths for the 2017 exams. = (—3,—l),Q = (l, 4). a) How long does it take to get to the destination? b) How long does it take to return to the starting point?. Triple Scalar Product. You travel 25 meters east and then travel 48 meters south. uk Vectors (H) - Version 2 January 2016 Given that MNC is a straight line, find the value of k. (c)The number of students at Harvard. Aboypullsawagonwithaforceof6Neastasanotherboypushesitwithaforceof4N east. 1 Vectors: Geometric Approach What’s a vector? in elementary calculus and linear algebra you probably de ned vectors as a list of numbers such as ~x = (4;2;5) with special algebraic manipulations rules, but in elementary physics vectors were probably de ned as ‘quantities that have both a magnitude and a direction such as. Find worksheet stock images in HD and millions of other royalty-free stock photos, illustrations and vectors in the Shutterstock collection. 5 meters: A B!Determine the magnitude of the following vector sums:!a. Unit 1 - Vector Kinematics. Show all of your work. The following is a list of worksheets and other materials related to Math 223 at the UA. In this handout, unit vectors will be written the same way as regular vectors, but with a hat on top of it them. Introduction To Vectors. Starting from Spain and travelling west (or bearing 270), draw one vector for each month of travel using your red pencil. Sequences and Series Sequences #1 ( Harder) Sequences and Series #2 ( Harder) Functions - Domain and Range - Composite. This worksheet will walk you through some basic vector operations. Practice Problem Set F=ma FORCE = MASS x ACCELERATION. Two vectors of the same magnitude are added; one pointing east, one west. Questions and Revision GCSE Maths Level 6 Level 7 Vectors. In your helper application worksheet, you will find the vectors 1, t, t 2, and y for the U. Topic is actually a complete lesson in a unit or even small sub-topic. • you’re dealing with exactly 3 vectors. Download, Fill In And Print Vector Addition Worksheet With Answers Pdf Online Here For Free. Physics 2204 Name:_____ Unit 1 Worksheet #2 ( Scalars vs Vectors, and Vector Addition) 1. An algebra is a set of mathematical rules. Examples of vectors are velocity, acceleration, force, momentum etc. Given that c 2a and d 3b. All of our worksheets are free for use by teachers, students, homeschool parents teaching calculus, or anyone using them in an educational setting. Tes Global Ltd is registered in England (Company No 02017289) with its registered office at 26 Red Lion Square London WC1R 4HQ. Second Conditional Speaking Activities PDF. and denote vectors by lower case boldface type such as u, v, w etc. Scalars and quantities that are a number and a unit; vectors are a number and a unit plus a direction. What are Scalar and Vector Quantities? Some of the quantities that we have talked about in the Forces and Motion chapter are scalars and some are vectors. Vector Operations: Practice Problems EXPECTED SKILLS: Be able to perform arithmetic operations on vectors and understand the geometric consequences of the operations. The math worksheets are randomly and dynamically generated by our math worksheet generators. The graph of the vector !v = h2;3iis at right. Anatomy Coloring pages. Improve your math knowledge with free questions in "Add vectors" and thousands of other math skills. Worksheet 4: Putting it all together. Download Worksheet design for subtraction Vector Art. Components of a vector. 0 MARKS ANSWER ALL QUESTIONS. This allows you to make an unlimited number of printable math worksheets to your specifications instantly. Past Paper Questions - Vectors. Mr Trask's Physics Website Mr Trask's Physics Trigonometry, Vectors and Graphing. Entering text in a document is easy. The displacement of the boat from. 12/11/2017; 5 minutes to read; In this article. Sketch the plane parallel to the xy-plane through (2;4;2) 2. Add vectors that are not colinear and are not perpendicular. Vectors are quantities that have both magnitude and direction. population data. 14 (a) Use the inverse tangent function to find the distance angle : 1 9. Ahrens 2/18/2006 9. When adding vectors graphi-cally, put the arrows head to tail. Dec 06, 2013 · like if your a furry rawr xd lul rofl <3 lol lul UwU uWu 0w0 kiss kiss. Title: Vectors and Scalars 1 Vectors and Scalars. Name _____ Vector Addition Worksheet (Linfield Summer) Directions: Add each pair of vectors shown below in its box, making sure to show the vector addition as well as the resultant with a dotted line and arrowhead. Write the word or phrase that best completes each statement or answers the question. Thousands of new, high-quality pictures added every day. Worksheet 5: linear independence 1{4. Addition and Subtraction of Vectors 1 Appendix A Addition and Subtraction of Vectors In this appendix the basic elements of vector algebra are explored. Videos, Practice Questions and Textbook Exercises on every Secondary Maths topic. Make copies of the Vector Voyage Worksheet 1 and Vector Voyage Worksheet 2, one each per student. For example, the vector 5 i - 3 j would look something like this on a diagram: Adding Vectors. Sketch the specified vector. Vectors : Forms , Notation , and Formulas A scalar is a mathematical quantity with magnitude only (in physics, mass, pressure or speed are good examples). worksheet-addition. Choose from over a million free vectors, clipart graphics, vector art images, design templates, and illustrations created by artists worldwide!. The Graphical Addition of Vectors A wide variety of physical quantities are described by vectors. Describe a vector and calculate displacement among other things for the quiz. Also use congruency marks to indicate which vectors are equal in magnitude. Vectors are mathematical quantities used to represent concepts such as force or velocity which have both a magnitude and a direction. Marks UCSD Borrows heavily from: •A set of vectors is linearly dependent if one of the vectors can be expressed as a linear. Draw a line that gives the vertical length of this. The so-called parallelogram law gives the rule for vector addition of two or more vectors. Stop searching. Question 3. 98 jF yj=30sin30=15. Physics 2204 Name:_____ Unit 1 Worksheet #2 ( Scalars vs Vectors, and Vector Addition) 1. The graph of the vector !v = h2;3iis at right. N of W, S, S of E, etc. 5th Form Worksheets for Vectors and Matrices. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4. Because many of these problems involve more than two vectors a drawing is very important. Position vectors are vectors giving the position of a point, relative to a fixed point (the origin). The diagonal from the initial point to the opposite vertex of the parallelogram is the resultant. b) Use the “tip-to-tail” triangle method to draw A-B. The sum of two vectors is the vector obtained by lining up the tail of one vector to the head of the other: (6 problems) When an object has a velocity relative to a moving medium, it's net velocity is the sum of it's relative velocity and the medium's velocity. Anatomy Coloring pages. It can be represented by a dot product: where F is the applied force which may or may not be entirely in the same direction as s, the distance the object moves. You travel 25 meters east and then travel 48 meters south. Download Free 3d Vectors and other types of 3d graphics and clipart at FreeVector. acceleration. B is the mid point of OC OA a and 0B = b. All of our worksheets are free for use by teachers, students, homeschool parents teaching calculus, or anyone using them in an educational setting. Concluding and Applying. Remember that a vector is specified by its direction and magnitude, so that the two arrows of equal length pointing to the west represent the same vector, while the three arrows of equal length pointing to the north-east also represent the same vector. Diagram NOT accurately drawn OAB is a triangle. In this chapter, we will study some of the basic concepts about vectors, various operations on vectors, and their algebraic and geometric properties. Stop searching. P, Q, R and S are the midpoints of OX, XY, YZ and OZ respectively. 2) To find magnitude and direction of vectors from components. Draw PQ in a coordinate plane. Vector Magnitude and Direction Name: _____ Period: _____ Date: _____ Answer the following questions and show all work. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4. An introduction to vectors by David Frank and Duane Q. The vectors AA, BB uuuruuur represent the zero vector, Unit Vector A vector whose magnitude is unity (i. Bert and Ernie are trying to drag a large box on the ground. Printable Math Worksheets @ www. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. Remember, mass is in kg - - force in in N (newtons) - - acceleration is in m/s2. For the given vectors u and v, evaluate the following expressions. Sample Learning Goals Describe a vector in your own words; Explain a method to add vectors. When two vectors are perpendicular, the addition can be. A set of vectors is said to be mutually orthogonal if the dot product of any pair of distinct vectors in the set is 0. 1 – Kinematics in 1D Break up the following vectors into their components that are perpendicular and parallel to the slope components i. He wants it to travel due North but the fan is blowing into the sail West at 3. 4 9/7/2009. Express the force vector F in terms of i and j. 0o] W of S C = 2. With the Students. Free Online Alevel, GCSE, Secondary, 11+ Maths Resources, Past Exam Papers, Worksheets, Specimen, Solution Videos, Online Test, Online Self-Assessment GCSE Vectors 2 Worksheet Book Free Consultation. There may be circumstances in which you need to extract a vector from a matrix or to convert a matrix to a vector. 60 x 103 kg car traveling at 20. Then draw lines to form a complete parallelogram. A complete set of Class Notes, Handouts, Worksheets, PowerPoint Presentations, and Practice Tests. Vector Addition (1-dimensional vectors) Adding 1-dimensional Vectors. • Vector Voyage Solution Worksheet 1 • Vector Voyage Solution Worksheet 2 • Vector Voyage Solution Worksheet 3 Troubleshooting Tips Getting started drawing the vectors may be confusing for students. vectors worksheets pg 1 of 13 vectors 15 Draw a vector's horizontal and vertical components. = (—3,—l),Q = (l, 4). The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other and multiplying it times the magnitude of the other vector. Vectors can be added and subtracted. The displacement of the boat from. For example, the vector 5 i - 3 j would look something like this on a diagram: Adding Vectors. When adding vectors graphi-cally, put the arrows head to tail. When expressing a quantity we give it a number and a unit (for example, 12 kg), this expresses the magnitude of the quantity. The ways that the components of a vector can be written in Matlab will be introduced. !Given the three vectors shown below: 60. Construct a non-zero vector perpendicular to each of the pairs of vectors A, C in question 21. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4. Aug 09, 2019 · Vectors are a foundational element of linear algebra. 1) View Solution. How did you connect the arm to the NXT robot? Did you use a motor to grab the marker? 4. This formula uses the dot product, magnitude and cosine to give us the angle between vectors. Grade 9 Math Vectors. See what you know about math with vectors via this worksheet and quiz. Home > By Grade > 8th Grade Math Worksheets; The math worksheets and other resources below are listed by subject have been aligned with the 8th Grade level based on the Common Core Standards For Mathematics. A complete set of Class Notes, Handouts, Worksheets, PowerPoint Presentations, and Practice Tests. VECTORS WORKSHEETS pg 1 of 13. True or False: An object moving for 10s can still have zero displacement? 2. For each of the 5 following. Linear Algebra Worksheet 3. 1b, for each pair of points below: i plot the points on the axes ii write down a vector joining the two points. Express the force vector F in terms of i and j. The direction vectors of the lines are i – 2j + k and 3i – 3j + 5k. Remember that a vector is specified by its direction and magnitude, so that the two arrows of equal length pointing to the west represent the same vector, while the three arrows of equal length pointing to the north-east also represent the same vector. This material is taught in MATH109. Leading to: After the introduction of displacement as one vector example, the next vector introduced is velocity, followed by force, to show that many physical quantities are vectors.