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  • Find the coordinates of the points which trisect the line segment AB , given that A(2,1,-3) and B(5,-8,3).

Find the coordinates of the points which trisect the line segment AB , given that A(2,1,-3) and B(5,-8,3).

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Solution:  Let P and Q be the points which trisect AB . Then , AP=PQ=QB . Therefore , P divides AB in the ratio 1:2 and Q divides it in the ratio 2:1. 

                As P divides AB in the ratio 1:2 . so coordinates of P are 

               (frac1 imes5+2 imes21+2, frac1 imes-8+2 imes11+2,frac1 imes3+2 imes-31+2)  or   ,   (3,-2,-1)

              Since Q divides AB in the ratio 2:1 . so coordinates of Q are 

           (frac2 imes5+1 imes22+1,frac2 imes-8+1 imes12+1,frac2 imes3+1 imes-32+1)       or  , (4,-5,1) 

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Deependra Verma

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