What is the projection of $<-2,4,2 >$ onto $<1,8,-3 >$ ?

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Answer 1 · 2017-10-14T09:11:24

The projection is $=12/37<1,8,-3>$

Let the vectors be

$vecu=<-2,4,2>$

and

$vecv=<1,8,-3>$

The projection of $vecu$ onto $vecv$ is

$proj_(vecv)vecu=(vecu.vecv)/(||vecv||^2)vecv$

$=(<-2,4,2>.<1,8,-3>)/(||<1,8,-3>||^2)<1,8,-3>$

$=(-2+32-6)/(1+64+9)<1,8,-3>$

$=24/74<1,8,-3>$

$=12/37<1,8,-3>$

What is the projection of <-2,4,2 ><-2,4,2 > onto <1,8,-3 ><1,8,-3 >?