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Respect (88%):
Date Posted: 7/23/2008 5:26:53 PM  Status: Live
linear algebra
Course Textbook Chapter Problem
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Question Details:
Prove  if and only if u and v have the same direction.
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Date Posted: 7/23/2008 7:13:56 PM  Status: Live
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Response:
If u and v have the same direction then <u,v> = cosθ||u||||v|| = ||u||||v|| so ||u + v||2 = <u +v, u + v> = ||u||2 + ||v||2 + 2<u,v> = ||u||2 + ||v||2 + 2||u||||v|| = (||u|| + ||v||)2
If (||u|| + ||v||)2 = ||u + v||2 then <u,v> = ||u||||v|| so cosθ=1 and θ=0 so u and v have the same direction.
rox636's Comment:
thank you so much!



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