(Rules for dot products) These equations are simple but useful: (1) v • w = w • v (2) u · (v + w) = u•v +u•w (3) (cv) • w = • w = c(v • w) Use (2) with u = v + w to prove ||v + w||² = v • v + 2v •w + w• w.
(Rules for dot products) These equations are simple but useful: (1) v • w = w • v (2) u · (v + w) = u•v +u•w (3) (cv) • w = • w = c(v • w) Use (2) with u = v + w to prove ||v + w||² = v • v + 2v •w + w• w.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(Rules for dot products) These equations are simple but useful:
u・v+u・w (3) (cv) • w =
·
=u•v+u•w c(v • w)
(1) v • w = w • v (2) u (v + w) =
Use (2) with u = v + w to prove ||v + w||² = v • v + 2v・w + w・w.
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