1.2 Dot Product and Orthogonality

# 1.2 Dot Product and Orthogonality - Dot Product and...

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Dot Product and Orthogonality The Norm Dot Product Properties The Angles Between Two Vectors Dot Product and Orthogonality September 8, 2007 Previous Slide Back Forward Next Slide

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Dot Product and Orthogonality The Norm Dot Product Properties The Angles Between Two Vectors The norm or length of a vector Let v = ( v 1 , v 2 , . . . , v n ) be a vector in R n . We deﬁne its norm or length by the formula k v k = q v 2 1 + v 2 2 + . . . + v 2 n . Compare with the usual distance in R 2 or R 3 . Previous Slide Back Forward Next Slide
Dot Product and Orthogonality The Norm Dot Product Properties The Angles Between Two Vectors Example If v = (2 , 1 , 1 , - 1 , 5) in R 5 ﬁnd k v k . Previous Slide Back Forward Next Slide

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Dot Product and Orthogonality The Norm Dot Product Properties The Angles Between Two Vectors A unit vector is a vector of length 1. Previous Slide Back Forward Next Slide
and Orthogonality The Norm Dot Product Properties The Angles Between Two Vectors Example Find a unit vector that points in the same direction as v = (3 , 4). Previous Slide

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## This note was uploaded on 04/18/2008 for the course LINEAR ALG 040 taught by Professor Dillhion during the Spring '08 term at UWO.

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1.2 Dot Product and Orthogonality - Dot Product and...

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