[" The angle between the vectors a and "b" having "],[" direction ratios "(-p,1,-2)" and "(2,-p,-1)" is "(pi)/(3)," then "],[" the value of "p" is "]

If the angle between the vectors bar a and bar b having direction ratios 1, 2, 1 and 1, 3k, 1 is (pi)/(4) , then k =

If the angle between the lnes with direction ratios (3,4,x) and (2,-1,4) is pi/2 then the value of x is

Find the angle between the lines whose direction ratios are p, q, r and q-r, r-p, p-q

Two events A and B are mutually exclusive, if P(A)= (1)/(2) and P(A cup B) = (2)/(3) , then the value of P(B) is -

A plane P_(1) has the equation 4x-2y+2z=3 and P_(2) has the equation -x+ky-2z=7 . If the angle between P_(1) and P_(2) is (2pi)/(3) , then the value of k can be

A plane P_(1) has the equation 4x-2y+2z=3 and P_(2) has the equation -x+ky-2z=7 . If the angle between P_(1) and P_(2) is (2pi)/(3) , then the value of k can be

If the direction ratios of two parallel lines are 4, -3, -1 and p + q, 1 + q , 2, then find the values of p and q.