Q69 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Mathematics

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 $M)=$

  • Correct answer
    A
    $5 \hat{i}-5 \hat{j}+3 \hat{k}$
  • B
    $11 \hat{i}-13 \hat{j}-11 \hat{k}$
  • C
    $5 \hat{i}+5 \hat{j}-3 \hat{k}$
  • D
    $11 \hat{i}+13 \hat{j}-11 \hat{k}$

Solution

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 $5(\overline{\mathrm{OC}})-2(\overline{\mathrm{OM}})=5 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$

Hence, the correct answer is option: 'A'.

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