What is the projection of $(3i + 2j - 6k)$ onto $(-2i- 3j + 2k)$ ?

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Answer 1 · 2017-11-06T07:54:18

The projection is $= <48/17,72/17,-48/17>$

Let $vecb=<3,2,-6>$ and $veca=<-2,-3,2>$

The projection of $vecb$ onto $veca$ is

$proj_(veca)vecb=(veca.vecb)/(||veca||^2)veca$

$veca.vecb = <-2,-3,2> . <3,2,-6> = (-2) * (3)+(-3) * (2)+(2) * (-6) = -6-6-12=-24$

$||veca||=||<-2,-3,2>||=sqrt((-2)^2+(-3)^2+(-2)^2)=sqrt(4+9+4) = sqrt17$

Therefore,

$proj_(veca)vecb=(veca.vecb)/(||veca||^2)veca=-24/17 <-2,-3,2>$

What is the projection of (3i + 2j - 6k)(3i + 2j - 6k) onto (-2i- 3j + 2k) (-2i- 3j + 2k)?