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Unformatted text preview: ±u and get proj ±u ( ±v ) = ±u · ±v  ±u  2 ±u. 4 For the unit vector in the direction of [3 ,1] , we ﬁnd  ±u  = √ 9 + 1 = √ 10 , and for the dot product we have ±u · ±v = [1 ,1] · [3 ,1] = 3 + 1 = 4 , so proj ±u ( ±v ) = ±u · ±v  ±u  2 ±u = 4 10 ±u = 2 5 [3 ,1] . For the start of Section 1.3, we use the vector form of the equation of a line ±x = ± p + t ± d, where ± p is a point on the line, ± d is the direction vector of the line, and ±x is in R 2 or R 3 . See the text Example 1.20, pg. 3233, for discussion. When the point on the line is (1 , 3) and the direction is ± d = [1 ,2] , we get ±x = [ x, y ] = [1 , 3] + t [1 ,2] , which we write in terms of components as x = 1 + t, y = 32 t....
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 Spring '08
 Dodson
 Math, Linear Algebra, Vector Space, Dot Product, Mon

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