Q. 2 E5.0( 1 Vote )

# Using vector method, prove that the following points are collinear.A (2, –1, 3), B (3, –5, 1) and C (–1, 11, 9).

A (2, –1, 3), B (3, –5, 1) and C (–1, 11, 9).

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

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Know All About Types of Relations53 mins
Interactive Quiz on Properties of Determinants43 mins
Determinants of Matrices of different order59 mins
Battle of Graphs | various functions & their Graphs48 mins
Triangular Matrices & operations on matrices58 mins