Find the value of `a`, if the vectors `i - 2j + k and ai - 5j + 3k and 5i - 9j + 4k` are coplanar.

If vectors i + j + k,i - j+k and 2i + 3j + mk are coplanar, then m =

The value of alpha for which the vectors 2i-j+k, i+2j+alphak" and "3i-4j+5k are coplanar is

The sum of the distinct real values of mu for which the vectors mu i+j+k , i+mu j+k , i+j+mu k are coplanar is

If the vectors ai +j + k , i-bj+k, i+j-ck are co-planar, then abc + 2 =

If vectors 2i - j + k, i + 2j - 3k and 3i + mj + 5k are coplanar, then m is a root of the equation

Values of a for which the points A, B, C with position vectors 2i - j+k, i - 3j - 5k and ai - 3j +k, respectively, are the vertices of a right angled triangle with C = (pi)/2 are

The value of p so that vectors 2hat i-hat j+hat k , hat i+2hat j-3hat k and 3hat i+phat j+5hat k are coplanar is

The value of scalar triple product i-2j+3k, 2i+j-k" and "j+k is

if theta angle between two vectors 2i+j+7k and i+5j+k then cos theta