What is the projection of $<-5,2,8>$ onto $<4,-6,3 >$ ?

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Answer 1 · 2018-01-26T10:55:13

The projection is $=-8/sqrt61<4, -6,3>$

The vector projection of $vecb$ onto $veca$ is

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

$veca=<4,-6,3>$

$vecb= <-5, 2,8>$

The dot product is

$veca.vecb =<4,-6,3>. <-5,2,8>$

$= (4)*(-5)+(-6) *(2)+(3)*(8)=-20-12+24=-8$

The modulus of $veca$ is

$=||veca||=||<4,-6,3>|| =sqrt((4)^2+(-6)^2+(3)^2)=sqrt61$

Therefore,

$proj_(veca)vecb=-8/sqrt61<4, -6,3>$

What is the projection of <-5,2,8><-5,2,8> onto <4,-6,3 ><4,-6,3 >?