Explanation Approach: The dot product of two vectors u and v can be found by using the formula, u ⋅ v = ‖ u ‖ ‖ v ‖ cos θ . Here, θ ∈ [ 0 , π ] is the angle between the standard position vectors of u and v . Given Information: Two non-zero vectors u and v such that u ⋅ v = 0 . Calculation: u ⋅ v = ‖ u ‖ ‖ v ‖ cos θ ⇒ 0 = ‖ u ‖ ‖ v ‖ cos θ The magnitude of a non-zero vector can never be zero To determine b) To explain: The angle θ between two non-zero vectors u and v , if u ⋅ v > 0 . To determine c) To explain: The angle θ between two non-zero vectors u and v , if u ⋅ v < 0 .

10th Edition

ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 6.4, Problem 90E

To determine

a)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v=0.

To determine

b)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v>0.

To determine

c)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v<0.

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Chapter 6.4, Problem 89E

Chapter 6.4, Problem 91E

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Chapter 6 Solutions

Precalculus (MindTap Course List)

Ch. 6.1 - Checkpoint For the triangle shown, A=30, B=45, and...Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E

Knowledge Booster

a) To explain: The angle θ between two non-zero vectors u and v , if u ⋅ v = 0 .

Solution Summary: The author explains the angle theta between two non-zero vectors u and v.

a)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v=0.

b)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v>0.

c)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v<0.

Want to see the full answer?

Chapter 6 Solutions

a) To explain: The angle θ between two non-zero vectors u and v , if u ⋅ v = 0 .

Solution Summary: The author explains the angle theta between two non-zero vectors u and v.

a) To explain: The angle θ between two non-zero vectors u and v, if u⋅v=0.

b) To explain: The angle θ between two non-zero vectors u and v, if u⋅v>0.

c) To explain: The angle θ between two non-zero vectors u and v, if u⋅v<0.

Want to see the full answer?

Chapter 6 Solutions

a)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v=0.

b)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v>0.

c)

To explain:

The angle θ between two non-zero vectors u and v, if u⋅v<0.