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

To check: The vectors u = 〈 0 , 4 , − 1 〉 and v = 〈 − 3 , − 5 , 9 〉 are orthogonal, parallel or neither.

To check: The vectors u = 〈 0 , 4 , − 1 〉 and v = 〈 − 3 , − 5 , 9 〉 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 48E

To determine

To check: The vectors u=〈0,4,−1〉 and v=〈−3,−5,9〉 are orthogonal, parallel or neither.

Expert Solution & Answer

Answer to Problem 48E

The vectors u=〈0,4,−1〉 and v=〈−3,−5,9〉 are neither parallel nor orthogonal.

Explanation of Solution

Given information:

The given vectors are u=〈0,4,−1〉 and v=〈−3,−5,9〉 .

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=〈0,4,−1〉 and v=〈−3,−5,9〉 linearly independent.

Therefore, v=cu is not possible for any value of c . So, the vectors u=〈0,4,−1〉 and v=〈−3,−5,9〉 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=〈0,4,−1〉 and v=〈−3,− u⋅v=〈0,4,−1〉⋅〈−3,−5,9〉=0×−3+4×−5+(−1)×9=0−20−9=−295,9〉 .

As the dot product of both the vectors u=〈0,4,−1〉 and v=〈−3,−5,9〉 is non-zero. So, the vectors u=〈0,4,−1〉 and v=〈−3,−5,9〉 are not orthogonal.

Therefore, the vectors u=〈0,4,−1〉 and v=〈−3,−5,9〉 are neither parallel nor orthogonal.

Chapter 10.2, Problem 47E

Chapter 10.2, Problem 49E

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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