Q. 65.0( 1 Vote )

If <span lang="EN

Answer :

Let us understand that, two more points are said to be collinear if they all lie on a single straight line.


Given:


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 .




…(i)


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.


So, …(ii)


Similarly,
…(iii)


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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