Question

If `bar(OA)= hat(i) +3hat(J)-2hat(K), "then" bar(OC)` which bisects the angle AOB is given by:
A. `hat(i)-hat(J)-hat(K)`
B. `hat(i)+hat(J)+hat(K)`
C. `hat(-i)+hat(J)-hat(K)`
D. `hat(i)+hat(J)-hat(K)`

Answer 1

Correct Answer - 4
We know that internal bisector of the angle between the vectors bara and barb is
`therefore barOC = lambdabar(OA+barOB)`
`=lambda[hati+3hatj-2hatk)//sqrt(14)+(3hatj+hatj-2hatk)//sqrt(14)]`
`={lambda//sqrt(14)}(4hati + 4 hatj- 4 hat k)`
={4lamba//sqrt(14)}(hati+hatj-hatk)`
`"Taking" lambda = sqrt(14)//4barOC "can be taken as" (hati +hat j-hatk)`