If `vec(PO)+vec(OQ)=vec(QO)+vec(OR)`, prove that the points P, Q,R, are collinear.

If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R are collinear.

If vec PO+vec OQ=vec QO+vec OR, show that the point,P,Q,R are collinear.

If bar(PO)+bar(OQ)=bar(QO)+bar(OR), then prove that the points P,Q and R are collinear.

if vec(P) xx vec(R ) = vec(Q) xx vec(R ) , then

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

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

Let O be the origin and P, Q, R be the points such that vec(PO) + vec(OQ) = vec(QO) + vec(OR) . Then which one of the following is correct?

If vec AO+vec OB=vec BO+vec OC, prove that A,B,C are collinear points.

Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of them are collinear. If the vector (vec(a)+vec(b)) is collinear with the vector vec(c) and the vector (vec(b)+vec(c)) is collinear with vector vec(a) , then prove that (vec(a)+vec(b)+vec(c)) is a null vector.