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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

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

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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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