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High School Math Calculus PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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

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

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

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

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) .

Chapter 10.3, Problem 38E

Chapter 10.3, Problem 40E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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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