Show that the points whose position vectors are as given below are collinear :

and

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

Let us assume points to be A, B and C such that

Then, we need to find and .

And

Now, we need to draw a relation between and .

We know that,

Or

Or

This relation shows that and are parallel to each other.

But since, B is the common point in AB and BC.

⇒ AB and BC actually lies on a straight line.

Thus, A, B and C are collinear.