Let P be the point that divides the line segment AB in the ration AP:PB=m:n.

If O is the origin show that

OP=(n/m+n)OA + (m/m+n)OB

 Let O be the origin. The  , let  be the position vector of C which divides AB internally in the ratio m : n then,

                                       AC/CB = m/n                                                   

            =>        n.

            =>        n(P.V. of  – P.V. of ) = m(P.V. of  – P.V. of )