Q87 / 150 · MHT CET 2021 (24 Sep Shift 1) · Mathematics

The vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{k}}+4 \hat{\mathrm{k}}$ are the sies of a triangle $\mathrm{ABC}$. The length of the median through $\mathrm{A}$ is

  • Correct answer
    A
    $\sqrt{33}$ unit
  • B
    $\sqrt{288}$ unit
  • C
    $\sqrt{18}$ unit
  • D
    $\sqrt{72}$ unit

Solution

Let $\mathrm{A}$ be the origin. Then $\mathrm{B}=(3,0,4)$ and $\mathrm{C}=(5,-1,4)$ Mid point of $\mathrm{BC}=\left(\frac{3+5}{2}, \frac{0-2}{2}, \frac{4+4}{2}\right)$ i.e. $(4,-1,4)$ $\therefore$ Length of medium $=\sqrt{(4)^2+(-1)^2+(4)^2}=\sqrt{33}$

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

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