How do you find the scalar and vector projections of b onto a given $a = <3, -6, 2>$ , $b = <1, 1, 1>$ ?

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Answer 1 · 2016-11-14T14:35:32

The scalar projection is $=-1/7$
The vector projection is $=-1/49〈3,-6,2〉$

The scalar projection of $vecb$ onto $veca$ is

$=(veca.vecb)/(∥veca∥)$

$veca=〈3,-6,2〉$

$vecb=〈1,1,1〉$

$veca.vecb=〈3,-6,2〉.〈1,1,1〉=3-6+2=-1$

$∥veca∥=∥〈3,-6,2〉∥=sqrt(9+36+4)=sqrt49=7$

The scalar projection is $=-1/7$

The vector projection is $(veca.vecb)/(∥veca∥)^2veca$

$=-1/49〈3,-6,2〉$

How do you find the scalar and vector projections of b onto a given a = <3, -6, 2>a = <3, -6, 2>, b = <1, 1, 1>b = <1, 1, 1>?