If and are two non-collinear unit vectors such that 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

Find the values of x and y if the vectors and are mutually perpendicular vectors of equal magnitude.

If are two vectors such that then prove that is perpendicular to

In a triangle ΔOAB, _. If P and Q are points of trisection of AB, prove that