the properties of the dot product to show that for any vectors u and v. |u+v|²+ |u-v² = 2|u² +2|v|². lain by drawing a picture how this identity relates the lengths of the sides parallelogram spanned by vectors u and v to the lengths of the two onals. the properties of the dot product to show that the identity u + v² = |u²+ |v|² Funlain bu drowing a picture why this relation

Physics for Scientists and Engineers: Foundations and Connections
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ISBN:9781133939146
Author:Katz, Debora M.
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Chapter14: Static Equilibrium, Elasticity, And Fracture
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1. (a) Use the properties of the dot product to show that for any vectors u and v,
|u+v² + |u-v² = 2|u|² + 2/v².
Explain by drawing a picture how this identity relates the lengths of the sides
of a parallelogram spanned by vectors u and v to the lengths of the two
diagonals.
(b) Use the properties of the dot product to show that the identity.
|u + v² = |u|² + |v|²
holds exactly when u v= 0. Explain by drawing a picture why this relation
is the same as the Pythagorean theorem.
Transcribed Image Text:1. (a) Use the properties of the dot product to show that for any vectors u and v, |u+v² + |u-v² = 2|u|² + 2/v². Explain by drawing a picture how this identity relates the lengths of the sides of a parallelogram spanned by vectors u and v to the lengths of the two diagonals. (b) Use the properties of the dot product to show that the identity. |u + v² = |u|² + |v|² holds exactly when u v= 0. Explain by drawing a picture why this relation is the same as the Pythagorean theorem.
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