What is the projection of $< -3 , 1 ,3 >$ onto $< 4, 9, 1>$ ?

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Answer 1 · 2017-12-08T08:10:20

The vectors are perpendicular, no projection is possible.

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

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

Here,

$vecv= < -3,1,3>$ and

$vecu = <4,9,1>$

The dot product is

$vecu.vecv =<-3,1,3> . <4,9,1>$

$=(4*-3)+(9*1)+(3*1) =-12+9+3=0$

As the dot product is $=0$ , the $2$ vectors $vecu$ and $vecv$ are perpendicular, there is no projection.

What is the projection of < -3 , 1 ,3 >< -3 , 1 ,3 > onto < 4, 9, 1>< 4, 9, 1>?