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High School Math Calculus Precalculus with Limits: A Graphing Approach

The unit vector orthogonal to both u and v if u = ( i + 2 j ) and v = ( i − 3 k ) .

The unit vector orthogonal to both u and v if u = ( i + 2 j ) and v = ( i − 3 k ) .

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 10.3, Problem 36E

To determine

To find: The unit vector orthogonal to both u and v if u=(i+2j) and v=(i−3k) .

Expert Solution & Answer

Answer to Problem 36E

The unit vector orthogonal to both u and v is 17(−6i+3j−2k) .

Explanation of Solution

Given information:

The given value are u=(i+2j) and v=(i−3k) .

Calculation:

Calculate the cross product u×v .

u×v=(ijk12010−3)=i[(2)(−3)−(0)(0)]−j[(−3)(1)−(1)(0)]+k[(1)(0)−(2)(1)]=i(−6−0)−j(−3−0)+k(0−2)=−6i+3j−2k

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 of (u×v)⋅u .

(u×v)⋅u=〈−6,3,−2〉⋅〈1,2,0〉=(−6)(1)+(3)(2)+(−2)(0)=−6+6+0=0

Calculate the value of (u×v)⋅v .

(u×v)⋅v=〈−6,3,−2〉⋅〈1,0,−3〉=(1)(0)+(−3)(1)+(3)(1)=−6+0+6=0

Calculate the unit vector of u×v .

‖u×v‖=(−6)2+32+(−2)2=36+9+4=49=7

Calculate the unit vector orthogonal to both u and v .

u×v‖u×v‖=17(−6i+3j−2k)

Therefore, the unit vector orthogonal to both u and v is 17(−6i+3j−2k) .

Chapter 10.3, Problem 35E

Chapter 10.3, Problem 37E

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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