Is it true that if v and w are unit vectors, then v + w is a unit vector? Either show this is always true or provide examples to show that this is not always true.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 1CM
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Is it true that if v and w are unit vectors, then v + w is a unit vector? Either show this is always true or provide examples to
show that this is not always true.
Select all the appropriate counterexamples or "always true" if the statement is true for all v and w.
always true
counterexample: V and w are unit vectors making an angle of 60°
counterexample: v and w are unit vectors making an angle of 120°
counterexample: V and w are unit vectors making an angle of 90°
Transcribed Image Text:Is it true that if v and w are unit vectors, then v + w is a unit vector? Either show this is always true or provide examples to show that this is not always true. Select all the appropriate counterexamples or "always true" if the statement is true for all v and w. always true counterexample: V and w are unit vectors making an angle of 60° counterexample: v and w are unit vectors making an angle of 120° counterexample: V and w are unit vectors making an angle of 90°
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