Question

The position vectors of points A and B w.r.t. the origin are `veca=hati+3hatj-2hatk and vecb=3hati+hatj -2hatk`, respectively. Determine vector `vec(OP)` which bisects angle `AOB`, where P is a point on AB.

Answer 1

`|vec(OA)|= |vec(OB)| = sqrt(14)`
`Delta AOB` is isosceles. Hence, the bisector of angle `AOB` will bisect the base `AB`.
Hence, P is the midpoint `(2, 2, -2)` of AB. Therefore,
`" "vec(OP)= 2(hati+hatj-hatk)`