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

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Answer 1 · 2017-07-29T06:17:26

No projection since the vectors are perpendicular.

Let $vecb= <-1,1,1>$ and $veca= <1,-2,3>$

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

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

The dot product is

$veca.vecb=<-1,1,1> . <1,-2,3> =(-1*1)+(1*-2)+(1*3)$

$=-1-2+3=0$

The vectors $veca$ and $vecb$ are perpendicular.

So there is no projection posiible.

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