If and the coordinates of A are (0, - 2, - 1), find the coordinates of B.

If and are unit vectors inclined at an angle θ then prove that:

i.

ii.

The dot products of a vector with the vector and are 0, 5 and 8 respectively. Find the vector.

If A(2, 3, 4), B(5, 4, - 1), C(3, 6, 2) and D(1, 2, 0) be four points, show that is perpendicular to

Find the value of λ for which the vectors and are perpendicular to each other.