If prove that A, B, C are collinear points.

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

Given:

To Prove: A, B and C are collinear points.

Proof: We have been given that,

Rearrange it so that we get a relationship between and .

…(i)

Now, we know that

But actually we are doing , such that O is the point of origin so that the difference between the two vectors is a displacement.

So, …(ii)

Similarly,
…(iii)

Substituting equation (ii) & (iii) in equation (i), we get

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.

Hence, A, B and C are collinear.