Explanation Given: u = 2 i + j v = i − 2 j Approach: A vector v is represented in the terms of i , j , and k as, v = 〈 a 1 , a 2 , a 3 〉 = a 1 i + a 2 j + a 3 k Consider the two vectors u = 〈 u 1 , u 2 〉 and v = 〈 v 1 , v 2 〉 . The value of | u | is given by, | u | = u 1 2 + u 2 2 … ( 1 ) The value of u + v is given by, u + v = 〈 u 1 , u 2 〉 + 〈 v 1 , v 2 〉 = 〈 u 1 + v 1 , u 2 + v 2 〉 … ( 2 ) The value of u − v is given by, u − v = 〈 u 1 , u 2 〉 − 〈 v 1 , v 2 〉 = 〈 u 1 − v 1 , u 2 − v 2 〉 … ( 3 ) The value of 2 u is given by, 2 u = 2 〈 u 1 , u 2 〉 = 〈 2 u 1 , 2 u 2 〉 … ( 4 ) The value of 3 u − 2 v is given by, 3 u − 2 v = 3 〈 u 1 , u 2 〉 − 2 〈 v 1 , v 2 〉 = 〈 3 u 1 , 3 u 2 〉 − 〈 2 v 1 , 2 v 2 〉 = 〈 3 u 1 − 2 v 1 , 3 u 2 − 2 v 2 〉 … ( 5 ) Calculation: Since, u = 2 i + j and v = i − 2 j This can be written as, u = 〈 2 , 1 〉 and v = 〈 1 , − 2 〉 Substitute 2 for u 1 and 1 for u 2 in equation ( 1 ) . | u | = 2 2 + 1 2 = 4 + 1 = 5 Substitute 2 for u 1 , 1 for u 2 , 1 for v 1 and − 2 for v 2 in equation ( 2 ) .

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 9.CR, Problem 3E

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The given vector operations for the given u=2i+j, v=i−2j

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Chapter 9.CR, Problem 2E

Chapter 9.CR, Problem 4E

Chapter 9 Solutions

Algebra and Trigonometry

Ch. 9.1 - Prob. 1E Ch. 9.1 - CONCEPTS 2. a The length of a vector w=a1,a2 is...Ch. 9.1 - 38 Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - SKILLS 3-8 Sketching Vectors Sketch the vector...Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - 19-22Sketching VectorsSketch the given vector with...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - 27-30Writing Vectors in terms of i and jWrite the...Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - 31-36 Operations with vectors Find 2u, 3v, u+v,...Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 51E Ch. 9.1 - Prob. 52E Ch. 9.1 - Prob. 53E Ch. 9.1 - Components of a VelocityA jet is flying in a...Ch. 9.1 - Prob. 55E Ch. 9.1 - VelocitySuppose that in Exercise 55 the current is...Ch. 9.1 - VelocityThe speed of an airplane is 300 mi/h...Ch. 9.1 - Prob. 58E Ch. 9.1 - Prob. 59E Ch. 9.1 - Prob. 60E Ch. 9.1 - True Velocity of a JetFind the true speed and...Ch. 9.1 - Prob. 62E Ch. 9.1 - Prob. 63E Ch. 9.1 - Velocity of a Boat The boater in Exercise 63 wants...Ch. 9.1 - Prob. 65E Ch. 9.1 - Prob. 66E Ch. 9.1 - Prob. 67E Ch. 9.1 - Prob. 68E Ch. 9.1 - Prob. 69E Ch. 9.1 - Prob. 70E Ch. 9.1 - Prob. 71E Ch. 9.1 - Prob. 72E Ch. 9.1 - Prob. 73E Ch. 9.1 - Equilibrium of Tensions The cranes in the figure...Ch. 9.1 - Prob. 75E Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - 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How do we...Ch. 9.CR - Prob. 2CC Ch. 9.CR - Prob. 3CC Ch. 9.CR - Prob. 4CC Ch. 9.CR - Prob. 5CC Ch. 9.CR - Prob. 6CC Ch. 9.CR - Prob. 7CC Ch. 9.CR - Prob. 8CC Ch. 9.CR - Prob. 9CC Ch. 9.CR - Prob. 10CC Ch. 9.CR - Prob. 1E Ch. 9.CR - Prob. 2E Ch. 9.CR - Prob. 3E Ch. 9.CR - Prob. 4E Ch. 9.CR - Prob. 5E Ch. 9.CR - Prob. 6E Ch. 9.CR - Prob. 7E Ch. 9.CR - Prob. 8E Ch. 9.CR - Prob. 9E Ch. 9.CR - Prob. 10E Ch. 9.CR - Prob. 11E Ch. 9.CR - True Velocity of a PlaneAn airplane heads N60E at...Ch. 9.CR - Prob. 13E Ch. 9.CR - Prob. 14E Ch. 9.CR - Prob. 15E Ch. 9.CR - Prob. 16E Ch. 9.CR - Prob. 17E Ch. 9.CR - Prob. 18E Ch. 9.CR - Prob. 19E Ch. 9.CR - Prob. 20E Ch. 9.CR - Prob. 21E Ch. 9.CR - Prob. 22E Ch. 9.CR - Prob. 23E Ch. 9.CR - Prob. 24E Ch. 9.CR - Prob. 25E Ch. 9.CR - Prob. 26E Ch. 9.CR - Prob. 27E Ch. 9.CR - Prob. 28E Ch. 9.CR - Prob. 29E Ch. 9.CR - Prob. 30E Ch. 9.CR - Prob. 31E Ch. 9.CR - Prob. 32E Ch. 9.CR - Prob. 33E Ch. 9.CR - Prob. 34E Ch. 9.CR - Prob. 35E Ch. 9.CR - Prob. 36E Ch. 9.CR - Prob. 37E Ch. 9.CR - Prob. 38E Ch. 9.CR - Prob. 39E Ch. 9.CR - Prob. 40E Ch. 9.CR - Prob. 41E Ch. 9.CR - Prob. 42E Ch. 9.CR - Prob. 43E Ch. 9.CR - Prob. 44E Ch. 9.CR - Prob. 45E Ch. 9.CR - Prob. 46E Ch. 9.CR - Prob. 47E Ch. 9.CR - Prob. 48E Ch. 9.CR - Prob. 49E Ch. 9.CR - Prob. 50E Ch. 9.CR - Prob. 51E Ch. 9.CR - Prob. 52E Ch. 9.CR - Prob. 53E Ch. 9.CR - Prob. 54E Ch. 9.CT - TEST Let u be the vector with the initial point...Ch. 9.CT - TEST Let u=1,3 and v=6,2. a Find u3v. b Find...Ch. 9.CT - Prob. 3CT Ch. 9.CT - Prob. 4CT Ch. 9.CT - Prob. 5CT Ch. 9.CT - Prob. 6CT Ch. 9.CT - Prob. 7CT Ch. 9.CT - Prob. 8CT Ch. 9.CT - Prob. 9CT Ch. 9.CT - Prob. 10CT Ch. 9.CT - Prob. 11CT Ch. 9.FOM - Prob. 1P Ch. 9.FOM - 1-6 Sketch the vector field F by drawing a diagram...Ch. 9.FOM - 1-6 Sketch the vector field F by drawing a diagram...Ch. 9.FOM - 1-6 Sketch the vector field F by drawing a diagram...Ch. 9.FOM - Prob. 5P Ch. 9.FOM - Prob. 6P Ch. 9.FOM - Prob. 7P Ch. 9.FOM - Prob. 8P Ch. 9.FOM - Prob. 9P Ch. 9.FOM - Prob. 10P Ch. 9.FOM - Prob. 11P Ch. 9.FOM - Prob. 12P Ch. 9.FOM - Prob. 13P Ch. 9.FOM - Prob. 14P Ch. 9.FOM - Prob. 15P Ch. 9.FOM - Prob. 16P Ch. 9.FOM - Prob. 17P Ch. 9.FOM - Prob. 18P Ch. 9.FOM - Prob. 19P

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