Q. 2 B

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

A(2, –1, 3), B(4, 3, 1) and C(3, 1, 2)

Answer :

Given: A (2, –1, 3), B (4, 3, 1) and C (3, 1, 2).


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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