If and are two non-collinear vectors having the same initial point. What are the vectors represented by and

Given and are two non - collinear vectors having the same initial point.

Let and

Let us draw a parallelogram with AB and AD as any of the two sides of the parallelogram as shown below.

We know in parallelogram opposite sides are equal hence,

and

Now consider ΔABC, applying triangles law of vectors, we get

Similarly in ΔABD, applying triangles law of vectors, we get

Looking at the two equations (i) and (ii) we can conclude that

and are the diagonals of a parallelogram whose adjacent sides are and .