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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 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



 

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear student,

 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 )

 

 

 

 

 

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