The position vectors of the points P and...

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

`2(hati-hatj+hatk)`

`2hati+hatj-2hatk`

`2(-hati+hatj-hatk)`

`2(hati+hatj+hatk)`

Text Solution

Verified by Experts

The correct Answer is:

Since, `|OP|=|OQ|=sqrt(14),DeltaOPQ` is an isoscels.
Hence, the internal bisector OM is perpendicular to PQ and M is mid-point of P and Q. therefore,
`OM=(1)/(2)(OP+OQ)=2hati+hatj-2hatk`

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