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

If A, B, C and D are four non-collinear points in the plane such that bar(AD)+bar(BD)+bar(CD)=bar(0) , then prove that the points D is the centroid of the triangle ABC.

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

In the space A(bar(a)) is a point and bar(b) is a vector. If P(bar(r )) is any point such that bar(r ) xx bar(b) = bar(a) xx bar(b) then show that locus of P is a straight line.

Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b) . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 (i) internally.

Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b) . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 externally.

In the adjacent figure bar(OP) , bar(OQ) , bar(OR) and bar(OS) are four rays. Prove that anglePOQ+angleQOR+angleSOR+anglePOS=360^(@) .

In the adjacent figure bar(OP) , bar(OQ) , bar(OR) and bar(OS) are four rays. Prove that anglePOQ+angleQOR+angleSOR+anglePOS=360^(@) .