The position vectors of points `Aa n dB` w.r.t. the origin are ` vec a= hat i+3 hat j-2 hat k ,` respectively. Determine vector ` vec O P` which bisects angle `A O B ,` where `P` is a point on `A Bdot`

Explanation

`|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)`