Q72 / 150 · MHT CET 2024 (03 May Shift 2) · Mathematics

If the vectors $\overline{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$ and $\overline{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ are the sides of the triangle $A B C$, then the length of the median through A is

  • A
    $\sqrt{45}$ units
  • B
    $\sqrt{18}$ units
  • C
    $\sqrt{72}$ units
  • Correct answer
    D
    $\sqrt{33}$ units

Solution

Let $A D$ be the median of $\triangle A B C$. $\begin{aligned} \overline{\mathrm{AD}} & =\frac{\overline{\mathrm{AB}}+\overline{\mathrm{AC}}}{2} \\ & =\frac{8 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{2} \\ & =4 \hat{\mathrm{i}}-\hat{\mathrm{j}}+4 \hat{\mathrm{k}} \end{aligned}$ $\therefore|\overline{\mathrm{AD}}|=\sqrt{4^2+1^2+4^2}=\sqrt{33}$ units

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

Relevant Questions