Let us understand that, two more points are said to be collinear if they all lie on a single straight line.
To Prove: A, B and C are collinear points.
Proof: We have been given that,
Rearrange it so that we get a relationship between and .
Now, we know that
But actually we are doing , such that O is the point of origin so that the difference between the two vectors is a displacement.
Substituting equation (ii) & (iii) in equation (i), we get
Thus, 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.
Hence, A, B and C are collinear.
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