Prove that the points having position vectors are collinear.

Let us understand that, two more points are said to be collinear if they all lie on a single straight line.

Let the points be A, B and C having position vectors such that,

So, in this case if we prove that and are parallel to each other, then we can easily show that A, B and C are collinear.

Therefore, is given by

And is given by

Let us note the relation between and .

We know,

Or

Or [∵, ]

This relation shows that and are parallel to each other.

But also, is the common vector in and .

⇒ and are not parallel but lies on a straight line.

Thus, A, B and C are collinear.