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).

Answer :

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

To Prove: A, B and C are collinear.


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.

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
Know About finding the Adjoint & Inverse Of Matrix46 mins
Complex Numbers | Full chapter QuizFREE Class
Lecture on Product of Determinants58 mins
Determining a determinant63 mins
Types of Matrices & Properties51 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses