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

1 Answer
Nov 21, 2016

The projection is [(-1)/(3)][hati-hatj+hatk][13][ˆiˆj+ˆk].

Explanation:

Let us assume veca=(-hati+hatj+hatk)a=(ˆi+ˆj+ˆk) and vecb=(hati-hatj+hatk)b=(ˆiˆj+ˆk).
The projection of vector 'vecbb' on 'vecaa' =[(vecb.veca)/(|veca|^2)][veca]=⎢ ⎢b.aa2⎥ ⎥[a].
veca.vecb=a_1b_1+a_2b_2+a_3b_3=-1a.b=a1b1+a2b2+a3b3=1.
|veca|=sqrt[(-1)^2+(1)^2+(1)^2}=sqrt(3)a=(1)2+(1)2+(1)2=3.
Substitute the above values in the projection equation we get,
:. projection ofvecb on veca is [(-1)/(sqrt(3))^2][hati-hatj+hatk]=(-1/3)(hati-hatj+hatk).