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