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.

The position vectors of points A and B w.r.t. the origin are `veca=hat

1.	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» `\|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)`

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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.

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