# 3.6 - Section 3.6 Dot Products and Projections Definition...

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Section 3.6 Dot Products and Projections Definition of dot product Let u = u 1 u 2 and let v = v 1 v 2 . The dot product of u and v is: 11 2 2 uv u v u v •= + Let u = u 1 u 2 u 3 and let v = . v 1 v 2 v 3 The dot product of u and v is: u v = u 1 v 1 + u 2 v 2 + u 3 v 3

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u θ v Theorem Let θ be the angle between the vectors u and v . We always take 01 8 0 θ ≤≤ !! cos then u v u v •= cos uv = Corollary : The vectors u and v are orthogonal (i.e. perpendicular) if and only if 0 .
Corollary: for a vector u we have uu u =• or 2 u = i Why? If 1 2 3 u u   =  11 2 2 33 then u u u u u u u u •= + + Corollary: If θ is the angle between the vectors u and v then

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## This note was uploaded on 10/16/2009 for the course MATH 1114 at Virginia Tech.

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3.6 - Section 3.6 Dot Products and Projections Definition...

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