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

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

If and are two non-collinear unit vectors such that find

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

Prove that: If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.