LinAlg4.1.3

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The position vectors of A and B are 2{\bar  {i}}+{\bar  {j}}-{\bar  {k}},{\bar  {i}}+2{\bar  {j}}+3{\bar  {k}}\, respectively.Fidn the position vector of the point which divides the line segment AB in the ration 2:3.

Let C divide the line segment AB in the ratio 2:3.

Therefore,position vector of C={\frac  {2({\bar  {i}}+2{\bar  {j}}+3{\bar  {k}})+3(2{\bar  {i}}+{\bar  {j}}-{\bar  {k}})}{2+3}}\,

{\frac  {1}{5}}[2{\bar  {i}}+4{\bar  {j}}+6{\bar  {k}}+6{\bar  {i}}+3{\bar  {j}}-3{\bar  {k}}]\,

{\frac  {1}{5}}[8{\bar  {i}}+7{\bar  {j}}+3{\bar  {k}}]\,

{\frac  {8}{5}}{\bar  {i}}+{\frac  {7}{5}}{\bar  {j}}+{\frac  {3}{5}}{\bar  {k}}\,


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