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

1 Answer
SaiGanesh Gotetti
Nov 21, 2016

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 ofvecb on veca is [(-1)/(sqrt(3))^2][hati-hatj+hatk]=(-1/3)(hati-hatj+hatk).

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