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

1 Answer
Narad T.
Nov 6, 2016

The projection is =-5/7〈-5,1,3〉=−57⟨−5,1,3⟩

Explanation:

The vector projection of vecb→b onto veca→a is given by
=(veca.vecb)/(∥veca∥*∥veca∥)veca=→a.→b∥∥→a∥⋅∥→a∥∥→a

Here vecb=〈6,2,1〉→b=⟨6,2,1⟩ and veca=〈-5,1,3〉→a=⟨−5,1,3⟩

The dot product veca.vecb=〈-5,1,3〉.〈6,2,1〉=-30+2+3=-25→a.→b=⟨−5,1,3⟩.⟨6,2,1⟩=−30+2+3=−25

The modulus of veca=(∥veca∥=∥〈-5,1,3〉∥=sqrt(25+1+9)=sqrt35→a=(∥→a∥=∥⟨−5,1,3⟩∥=√25+1+9=√35

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

=-5/7〈-5,1,3〉

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