Q246 / 270 · NDA 2022 (Phase 1) · Mathematics

If $4 \hat{i}+\hat{j}-3 \hat{k}$ and $p \hat{i}+q \hat{j}-2 \hat{k}$ are collinear vectors, then what are the possible values of $p$ and $q$ respectively?

  • A
    4 , 1
  • B
    1 , 4
  • Correct answer
    C
    $\frac{8}{3}, \frac{2}{3}$
  • D
    $\frac{2}{3}, \frac{8}{3}$

Solution

$4 \hat{i}+\hat{j}-3 \hat{k}$ and $p \hat{i}+q \hat{j}-2 \hat{k}$ are collinear vectors $\begin{aligned} & \therefore \frac{4}{\mathrm{p}}=\frac{1}{\mathrm{q}}=\frac{-3}{-2} \Rightarrow P=\frac{2}{3} \times 4=\frac{8}{3} \\ & \text {and } \frac{1}{\mathrm{q}}=\frac{3}{2} \Rightarrow \mathrm{q}=\frac{2}{3}\end{aligned}$

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

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