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

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Answer 1 · 2016-05-30T07:53:52

The projection of a vector a onto vector b is given by

$proj_a b=(a*b)/absa^2 *a$

Hence

The dot product of $a=(-1,1,1)$ and $b=(1,-1,1)$ is

$a*b=-1-1+1=-1$

The magnitude of a is $absa=sqrt(-1^2+1^2+1^2)=sqrt3$

Hence the projection is

$proj_a b=-1/3*(-1,1,1)=(-1/3,1/3,1/3)=1/3*(-i+j+k)$

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