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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