Explanation Given information: The vectors are v 1 = 〈 4 , 6 〉 , v 2 = 〈 − 3 , − 6 〉 , v 3 = 〈 − 8 , 4 〉 and v 4 = 〈 10 , 15 〉 Explanation: Let v 1 = 〈 4 , 6 〉 , v 2 = 〈 − 3 , − 6 〉 , and v 3 = 〈 − 8 , 4 〉 and v 4 = 〈 10 , 15 〉 Let u and v are two vectors in space, u × v = 0 , if and only if u and v are parallel. Two vectors are parallel, if the angle between two vectors is either 0 o or 180 o Two find the angle between two vectors u and v , use formula cos θ = u ⋅ v ‖ u ‖ ⋅ ‖ v ‖ The angle between the vectors v 1 = 〈 4 , 6 〉 , v 2 = 〈 − 3 , − 6 〉 is, cos θ = v 1 ⋅ v 2 ‖ v 1 ‖ ⋅ ‖ v 2 ‖ = 〈 4 , 6 〉 ⋅ 〈 − 3 , − 6 〉 ‖ 〈 4 , 6 〉 ‖ ⋅ ‖ 〈 − 3 , − 6 〉 ‖ = − 12 − 36 52 ⋅ 45 = − 48 52 ⋅ 45 ⇒ θ = cos − 1 ( − 48 52 ⋅ 45 ) = 172.87 o The angle between the vectors v 1 and v 2 is 172.87 o which not either 0 o or 180 o Hence, the vectors v 1 and v 2 are not parallel The angle between the vectors v 2 = 〈 − 3 , − 6 〉 and v 3 = 〈 − 8 , 4 〉 is, cos θ = v 2 ⋅ v 3 ‖ v 2 ‖ ⋅ ‖ v 3 ‖ = 〈 − 3 , − 6 〉 ⋅ 〈 − 8 , 4 〉 ‖ 〈 − 3 , − 6 〉 ‖ ⋅ ‖ 〈 − 8 , 4 〉 ‖ = 24 − 24 45 ⋅ 80 = 0 45 ⋅ 80 ⇒ θ = cos − 1 ( 0 45 ⋅ 80 ) = 90 o The angle between the vectors v 2 and v 3 is 90 o which not either 0 o or 180 o Hence, the vectors v 2 and v 3 are not parallel The angle between the vectors v 1 = 〈 4 , 6 〉 , v 4 = 〈 10 , 15 〉 is, cos θ = v 1 ⋅ v 4 ‖ v 1 ‖ ⋅ ‖ v 2 ‖ = 〈 4 , 6 〉 ⋅ 〈 10 , 15 〉 ‖ 〈 4 , 6 〉 ‖ ⋅ ‖ 〈 10 , 15 〉 ‖ = 40 + 90 52 ⋅ 325 = 130 52 ⋅ 325

10th Edition

ISBN: 9780321979070

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 9, Problem 20CT

To determine

Which two vectors are parallel from v1=〈4,6〉, v2=〈−3,−6〉, v3=〈−8,4〉, and v4=〈10,15〉

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Chapter 9, Problem 19CT

Chapter 9, Problem 21CT

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Chapter 9 Solutions

Precalculus (10th Edition)

Ch. 9.1 - Plot the point whose rectangular coordinates are (...Ch. 9.1 - Prob. 3AYU Ch. 9.1 - 4. Draw the angle in standard position. Ch. 9.1 - tan 1 ( 1 )= ______ .Ch. 9.1 - Prob. 5AYU Ch. 9.1 - Prob. 6AYU Ch. 9.1 - For the point with polar coordinates ( 1, 2 ) ,...Ch. 9.1 - The point ( 5, 6 ) can also be represented by...Ch. 9.1 - True or False In the polar coordinates ( r, ) , r...Ch. 9.1 - True or False The polar coordinates of a point are...

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Which two vectors are parallel from v 1 = 〈 4 , 6 〉 , v 2 = 〈 − 3 , − 6 〉 , v 3 = 〈 − 8 , 4 〉 , and v 4 = 〈 10 , 15 〉

Solution Summary: The author explains how to determine which two vectors are parallel from v_1, if the angle between them is 0 or 180.

Which two vectors are parallel from v1=〈4,6〉, v2=〈−3,−6〉, v3=〈−8,4〉, and v4=〈10,15〉

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Chapter 9 Solutions