Home
Class 12
MATHS
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

A

`2(hati-hatj+hatk)`

B

`2hati+hatj-2hatk`

C

`2(-hati+hatj-hatk)`

D

`2(hati+hatj+hatk)`

Text Solution

Verified by Experts

The correct Answer is:
B
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`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find |vecaxxvecb| , if veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

The position vectors of the points A,B and C are hati+2hatj-hatk,hati+hatj+hatk and 2hati+3hatj+2hatk , respectively. If A is chosen as the origin, then the position vectors of B and C are

If veca=2hati-hatj-5hatk and vecb=hati+hatj+2hatk , then find scalar and vector product.

Find a unit vector perpendicular to each one of the vectors vec a =4hati -hatj +3hatk and vecb =3 hati +2hatj -hatk

The position vectors of two point charges of 2 nC each are (2hati + 3hatj - hatk) m and (3hati + 5hatj + hatk) m respectively. Magnitude of the coulombian force acting between them is........

The unit vector parallel to the resultant of the vectors vecA=2hati+4hatj+2hatk and vecB=-2hati+4hatj-hatk is

Find |vec(a)xx vec(b)| , if vec(a)=hati-7hatj+7hatk and vec(b)=3hati-2hatj+2hatk .