Using vector method, prove that the following points are collinear.

A(1, 2, 7), B(2, 6, 3) and C(3, 10 –1)

Given: A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1).

To Prove: A, B and C are collinear.

Proof:

Let us define position vectors. So,

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

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, proved that A, B and C are collinear.