If `P(0, 1, 0) and Q(0, 0 1)` are two points, then the projection of PQ on the plane `x+y+z=3` is

Options

A. 2
B. 3
C. `sqrt(2)`
D. `sqrt(3)`

Answer

C

Explanation

The projection of `PQ` on the given plane is `PQ cos theta` where `theta` is the angle between `PQ` and the plane.
Let `vecn` be a vector normal to the plane.
We have `vec(PQ)=-hatj+hatk` and `vecn=hati+hati+hatk`
`:.sin theta=(vec(PQ).vecn)/(|vec(PQ)||vecn|)=0impliesvec(PQ)` is parallel to the plane.
Hence projection of `vec(PQ)` on the given plane
`=|vec(PQ)|cos theta=|vec(PQ)|=sqrt(1+1)=sqrt(2)`