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High School Math Calculus Precalculus with Limits: A Graphing Approach

The angle θ between the vectors u = 〈 3 , − 1 , 3 〉 and v = 〈 − 3 , 6 , 7 〉 .

The angle θ between the vectors u = 〈 3 , − 1 , 3 〉 and v = 〈 − 3 , 6 , 7 〉 .

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10, Problem 31RE

To determine

To find: The angle θ between the vectors u=〈3,−1,3〉 and v=〈−3,6,7〉 .

Expert Solution & Answer

Answer to Problem 31RE

The angle θ between the vectors u=〈3,−1,3〉 and v=〈−3,6,7〉 is 70.01° .

Explanation of Solution

Given information:

The vectors are u=〈3,−1,3〉 and v=〈−3,6,7〉 .

Calculation:

The formula for angle between the vectors u and v .

cosθ=u⋅v‖u‖‖v‖

Calculate the dot product of vectors u=〈3,−1,3〉 and v=〈−3,6,7〉 .

u⋅v=〈3,−1,3〉⋅〈−3,6,7〉=3×−3+(−1)×6+3×7=−3−6+21=12

Calculate the magnitude of vector u=〈3,−1,3〉 .

‖u‖=(3)2+(−1)2+32=3+1+9=14

Calculate the magnitude of vector v=〈−3,6,7〉 .

‖v‖=(−3)2+62+72=3+36+49=88=222

Substitute the values in the formula for angle.

cosθ=u⋅v‖u‖‖v‖=1214×222=37777

The solution of the equation cosθ=37777 is the angle θ=70.01° .

Therefore, the angle θ between the vectors u=〈3,−1,3〉 and v=〈−3,6,7〉 is 70.01° .

Chapter 10, Problem 30RE

Chapter 10, Problem 32RE

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

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