What is the projection of $<-6,2,1 >$ onto $<-5,1,3 >$ ?

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Answer 1 · 2016-11-06T07:32:32

The projection is $=-5/7〈-5,1,3〉$

The vector projection of $vecb$ onto $veca$ is given by
$=(veca.vecb)/(∥veca∥*∥veca∥)veca$

Here $vecb=〈6,2,1〉$ and $veca=〈-5,1,3〉$

The dot product $veca.vecb=〈-5,1,3〉.〈6,2,1〉=-30+2+3=-25$

The modulus of $veca=(∥veca∥=∥〈-5,1,3〉∥=sqrt(25+1+9)=sqrt35$

$:.$ the projection $=-25/(sqrt35)^2〈-5,1,3〉=-25/35〈-5,1,3〉$

$=-5/7〈-5,1,3〉$

What is the projection of <-6,2,1 ><-6,2,1 > onto <-5,1,3 ><-5,1,3 >?