What is the projection of $<-6,1,5 >$ onto $<1,5,9 >$ ?

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Answer 1 · 2016-10-27T17:55:40

The projection is $〈11/27,55/27,99/27〉$

Let $vecb=〈-6,1,5〉$ and $veca=〈1,5,9〉$

Then, the vector projection of $vecb$ onto $veca$ is given by

$(veca.vecb)/(∣veca∣∣veca∣)*veca$

$veca.vecb$ is the dot product
and $∣veca∣$ is the modulus of the vector

the dot product is $veca.vecb=〈1,5,9〉.〈-6,1,5〉=-6+5+45=44$

$∣veca∣= sqrt(1^2+5^2+9^2)=sqrt(1+25+82)=sqrt108$

so the projection $=(44/108)〈1,5,9〉=(11/27)〈1,5,9〉=〈11/27,55/27,99/27〉$

What is the projection of <-6,1,5 ><-6,1,5 > onto <1,5,9 ><1,5,9 >?