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

To check: The vectors u = 2 i − 3 j + k and v = − i − j − k are orthogonal, parallel or neither.

To check: The vectors u = 2 i − 3 j + k and v = − i − j − k are orthogonal, parallel or neither.

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 10.2, Problem 50E

To determine

To check: The vectors u=2i−3j+k and v=−i−j−k are orthogonal, parallel or neither.

Expert Solution & Answer

Answer to Problem 50E

The vectors u=2i−3j+k and v=−i−j−k orthogonal to each other.

Explanation of Solution

Given information:

The given vectors are u=2i−3j+k and v=−i−j−k .

Calculation:

To check that two vectors u and v are parallel, check that v=cu , for any value of c . Both the vectors are u=2i−3j+k and v=−i−j−k linearly independent.

Therefore, v=cu is not possible for any value of c . So, the vectors u=2i−3j+k and v=−i−j−k are not parallel.

Check that two vectors u and v are orthogonal, check that u⋅v=0 .

Calculate the dot product of both the vectors u=2i−3j+k and v=−i−j−k .

u⋅v=(2i−3j+k)⋅(−i−j−k)=2×−1+(−3)×−1+(1)×−1=−2+3−1=0

As the dot product of both the vectors u=2i−3j+k and v=−i−j−k is zero. So, the vectors u=2i−3j+k and v=−i−j−k are orthogonal.

Therefore, the vectors u=2i−3j+k and v=−i−j−k orthogonal to each other.

Chapter 10.2, Problem 49E

Chapter 10.2, Problem 51E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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