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`.

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 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 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)

For any three sets A_1 , A_2 ,A_3 . Let B_1 = A_1 , B_2 = A_2 - A_1 and B_3 = A_3 - A_1 cup A_2 , then which of the following statement is always true ?

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of C is

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

The ratio in which the line segment joining points A(a_1,\ b_1) and B(a_2,\ b_2) is divided by y-axis is (a) -a_1: a_2 (b) a_1: a_2 (c) b_1: b_2 (d) -b_1: b_2

The condition for the lines with direction ratio a_1,b_1,c_1 and a_2,b_2,c_2 are perpendicular is -