The position vectors of the points P and Q with respect to the origin O are `veca = hati + 3hatj-2hatk and vecb = 3hati -hatj -2hatk`, respectively. If M is a point on PQ, such that OM is the bisector of POQ, then `vec(OM)` is

Options

A. `2(hati-hatj+hatk)`
B. `2 hati+hatj-2hatk`
C. `2(-hati+hatj-hatk)`
D. `2(hati+hatj+hatk)`

Answer

B

Explanation

Since `|vec(OP)| = |vec(OQ)| = sqrt(14), Delta OPQ` is isosceles.
Hence, the internal bisector OM is perpendicular to PQ and M is the midpoint of P and Q. Therefore,
`vec(OM) = (1)/(2) (vec(OP)+ vec(OQ))= 2hati+hatj-2hatk`