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If vec (A O)+ vec (O B)= vec (B O)+ vec...

If ` vec (A O)+ vec (O B)= vec (B O)+ vec (O C)` , prove that `A , B , C` are collinear points.

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Verified by Experts

We are given that

` vec (A O)+ vec (O B)= vec (B O)+ vec (O C)`

Also we know that `vec(AB)=-vec(BA)`

`rArr vec(AO)+vec(OB)=-vec(OB)+vec(OC)`

`rArr vec(OB)- vec (OA)= vec(OC)- vec(OB)`

`rArr vec(AB)= vec(BC)`

`therefore A,B,C` are collinear.
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