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

1 Answer
Nov 21, 2016

Answer:

The projection is #[(-1)/(3)][hati-hatj+hatk]#.

Explanation:

Let us assume #veca=(-hati+hatj+hatk)# and #vecb=(hati-hatj+hatk)#.
The projection of vector '#vecb#' on '#veca#' #=[(vecb.veca)/(|veca|^2)][veca]#.
#veca.vecb=a_1b_1+a_2b_2+a_3b_3=-1#.
#|veca|=sqrt[(-1)^2+(1)^2+(1)^2}=sqrt(3)#.
Substitute the above values in the projection equation we get,
#:.# projection of#vecb# on #veca# is #[(-1)/(sqrt(3))^2][hati-hatj+hatk]=(-1/3)(hati-hatj+hatk)#.