If show that the angle between the vectors and is given by

If are three non-coplanar vectors such that then show that is the null vector

If a vector is perpendicular to two non-collinear vectors and then is perpendicular to every vector in the plane of and .

Let and be vector such If and then find

Let and be three vectors. Find the values of x for which the angle between and is acute and the angle between and is obtuse