What is the projection of $<2,4,3 >$ onto $<-3,4,-1 >$ ?

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Answer 1 · 2017-11-29T07:13:19

The projection is $=7/26 <-3,4,-1>$

The vector projection of $vecv$ onto $vecu$ is

$proj_uv= (vec u. vecv ) /(||vecu||)^2*vecu$

Here,

$vecv= < 2,4,3>$ and

$vecu = <-3,4,-1>$

The dot product is

$vecu.vecv =<2,4,3> . <-3,4,1->$

$=(2*-3)+(4*4)+(3*-1) =-6+16-3=7$

The magnitude of $vecu$ is

$=||<-3,4,-1 >|| = sqrt((-3)^2+(4)^2+(-1)^2)$

$=sqrt(9+16+1)=sqrt26$

The vector projection is

$proj_uv=7/26* <-3,4,-1>$

What is the projection of <2,4,3 ><2,4,3 > onto <-3,4,-1 ><-3,4,-1 >?