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If $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ are the position vectors of the points $\mathrm{A}$ and $\mathrm{B}$ respectively, $\mathrm{C}$ divides $\mathrm{AB}$ in the ratio $2: 3$ and $\mathrm{M}$ is the mid-point of $\mathrm{AB}$, then 5 (position vector of $C)-2($ position vector of $M)=$
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$5 \hat{i}-5 \hat{j}+3 \hat{k}$
P.V. of point A and B are $(2,-1,1)$ and $(1,-3,-5), C$ divides $A B$ in the ratio $2: 3$ and $M$ is the mid-point of $A B$ $\Rightarrow 5(\overline{\mathrm{OC}})=(8,-9,-7)$ and $2(\overline{\mathrm{OM}})=(3,-4,-4)$ Now $5(\overline{\mathrm{OC}})-2(\overline{\mathrm{OM}})=5 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$
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