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

We have been given position vectors and .

Let

Also, let O be the initial point having position vector as

Now, let us find and .

is given by

is given by

We have as

[∵, ]

Thus, 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.

⇒ A and B are collinear.

Hence, and are collinear.