Two balls having linear momenta `vecp_(1)=phati` and `vecp_(2)=-phati, ` undergo a collision in fre space. There is no external force acting on the ball. Let `vecp_(1)^(')` and `vecp_(2)^(')` be their final moment. Which of the following option(s) is (are) NOT ALLOWED for an non zero value of `p,a_(1),a_(2),b_(1),b_(2), c_(1)` and `c_(2).`

Options

A. `vec(p_(1))'=a_(1)hati+b_(1)hatj+c_(1)hatk,vec(p_(2))'=a_(2)hati+b_(2)hatj`
B. `vec(p_(1))'=c_(1)hatk,vec(p_(2))'=c_(2)hatk`
C. `vec(p_(1))'=a_(1)hati+b_(1)hatj+c_(1)hatk,vec(p_(2))'=a_(2)hati+b_(2)hatj-c_(1)hatk`
D. `vec(p_(1))=a_(1)hati+b_(1)hatj,vec(p_(2))'=a_(2)hati+b_(1)hatj`

Answer

A, D