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

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Answer 1 · 2018-05-08T06:19:13

The projection is $=-2/3veci-4/9vecj+2/3veck$

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

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

Here

$veca= <3,2,-3>$

$vecb= <-1,1,1>$

The dot product is

$veca.vecb = <3,2,-3>. <-1,1,1> = -3+2-3=-4$

The maghitude of $veca$ is

$|veca|=|<3,2, -3>| = sqrt(9+4+9)=sqrt18$

Therefore,

$proj_(veca)vecb=-4/18 <3,2,-3>$

$=-2/9 <3,2,-3>$

$= <-2/3, -4/9, 2/3>$

$=-2/3veci-4/9vecj+2/3veck$

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