If `vecPQ +vecOQ =vecQO+vecOR`, prove that the points P,Q,R are collinear.

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

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

Prove that any three points on a circle cannot be collinear.

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_3=p vec r_1+q vec r_2, then show that p+q=1.

A point p moves such that p and the points (2,3)(1,5) are always collinear. Show that the locus of p is 2x+y-7=0

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an H P , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.

Assertion (A) : veca,vecb,vecc are the position vector of three collinear points then 2 veca=vecb+vecc Reason (R ) : Collinear points, have same direction

Determine whether the points are collinear. P(-2,3), Q(1,2), R(4,1)

Prove that q to p -= ~p to ~q

Prove that Q to P -= P to - Q