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.


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.


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