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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Chapter 10.3, Problem 39E
To determine

To find: The unit vector orthogonal to both u and v if u=(i+j−k) and v=(i+j+k) .

Expert Solution & Answer
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Answer to Problem 39E

The unit vector orthogonal to both u and v is 22(i−j) .

Explanation of Solution

Given information:

The given value are u=(i+j−k) and v=(i+j+k) .

Calculation:

Calculate the cross product u×v .

  u×v=(ijk11−1111)=i[(1)(1)−(1)(−1)]−j[(1)(1)−(1)(1)]+k[(1)(1)−(1)(1)]=i(1+1)−j(1+1)+k(1−1)=2i−2j

Calculate the dot product of u×v with u and v separately and if they will be equal to zero. So, they are orthogonal.

Calculate the value (u×v)⋅u .

  (u×v)⋅u=〈2,−2,0〉⋅〈1,1,−1〉=(2)(1)+(−2)(1)+(0)(−1)=2−2=0

Calculate the value of (u×v)⋅v .

  (u×v)⋅v=〈2,−2,0〉⋅〈1,1,1〉=(2)(1)+(−2)(1)+(0)(1)=2−2=0

Calculate the unit vector of u×v .

  ‖u×v‖=(2)2+(−2)2+(0)2=4+4=8=22

Calculate the unit vector orthogonal to both u and v .

  u×v‖u×v‖=122(2i−2j)=24(2i−2j)=22(i−j)

Therefore, the unit vector orthogonal to both u and v is 22(i−j) .

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Chapter 10.3, Problem 38E
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Chapter 10.3, Problem 40E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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