Q83 / 150 · MHT CET 2022 (07 Aug Shift 2) · Mathematics

A vector with magnitude of 3 units, which is perpendicular to each of the vectors $\bar{a}=3 \hat{i}+\hat{j}-4 \hat{k}$ and $\bar{b}=6 \hat{i}+5 \hat{j}-2 \hat{k}$, is given by

  • Correct answer
    A
    $\pm(2 \hat{i}-2 \hat{j}+\hat{k})$
  • B
    $\pm(2 \hat{i}+2 \hat{j}-\hat{k})$
  • C
    $\pm(2 \hat{i}-2 \hat{j}-\widehat{k})$
  • D
    $\pm(2 \hat{i}+2 \hat{j}+\hat{k})$

Solution

$\begin{aligned} & \text { The required vector }= \pm 3\left(\frac{\vec{a} \times \vec{b}}{|\vec{a} \times \vec{b}|}\right)= \pm \frac{3(18 \hat{i}-18 \hat{j}+9 \hat{k})}{\sqrt{18^2+18^2+9^2}} \\ & = \pm \frac{3(18 \hat{i}-18 \hat{j}+9 \hat{k})}{27}= \pm(2 \hat{i}-2 \hat{j}+\hat{k})\end{aligned}$

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

Relevant Questions