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).`

Two balls having linear momenta vecp_(1)=phati and vecp_(2)=-phati, undergo a collision in free space. There is no external force acting on the ball. Let vecp_(1)^(') and vecp_(2)^(') be their final momenta. 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).

Two balls , having linear momenta vec(p)_(1) = p hat(i) and vec(p)_(2) = - p hat(i) , undergo a collision in free space. There is no external force acting on the balls. Let vec(p)_(1) and vec(p)_(2) , be their final momenta. The following option(s) is (are) NOT ALLOWED for any non -zero value of p , a_(1) , a_(2) , b_(1) , b_(2) , c_(1) and c_(2) (i) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) , vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) (ii) vec(p)_(1) = c_(1) vec(k) , vec(p)_(2) = c_(2) hat(k) (iii) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) ,vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) - c_(1) hat(k) (iv) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) , vec(p)_(2) = a_(2) hat(i) + b_(1) hat(j)

Two balls , having linear momenta vec(p)_(1) = p hat(i) and vec(p)_(2) = - p hat(i) , undergo a collision in free space. There is no external force acting on the balls. Let vec(p)_(1) and vec(p)_(2) , be their final momenta. The following option(s) is (are) NOT ALLOWED for any non -zero value of p , a_(1) , a_(2) , b_(1) , b_(2) , c_(1) and c_(2) (i) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) , vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) (ii) vec(p)_(1) = c_(1) vec(k) , vec(p)_(2) = c_(2) hat(k) (iii) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) ,vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) - c_(1) hat(k) (iv) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) , vec(p)_(2) = a_(2) hat(i) + b_(1) hat(j)

The balls, having linear momenta vecp_1=vecpi and vecp_2_2=-vecpi , undergo a collision in free space. There is no external force acting on the balls. Let vecp'_1 and vec p'_2 be their final momenta.The following option (s) is (are) NOT ALLOWED for any non-zero value of p, a_1, a_2, b_1, b_2, c_1 and c_2 .

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

Consider two vectors vecp _(1) = 4 hati - 3 hatj + 5 hatk and vecp _(2) =- 6 hati + 3 hatj - 2 hatk . What is (vecp _(1) + vecp _(2)) . (vecp _(1) xx 5 vec p _(2)) ?

Let vecp = 3ax^(2) hati - 2(x-1)hatj, q=b(x-1)hati + xhatj and ab lt 0 . Then vecp and vecq are parallel for:

Let vecp = 3ax^(2) hati - 2(x-1)hatj, q=b(x-1)hati + xhatj and ab lt 0 . Then vecp and vecq are parallel for:

Two dipoles vecP_(1) and vecP_(2) are oriented as shown in the figure. Assuming dipole of dipole moment vecP_(2) to be placed at origin and dipole of moment vecP_(1) is at a distance 'd' from origin then