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

1 Answer
May 8, 2018

Answer:

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

Explanation:

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#