Q244 / 270 · NDA 2023 (Phase 2) · Mathematics

The vectors $60 \hat{i}+3 \hat{j}, \quad 40 \hat{i}-8 \hat{j} \& \beta \hat{i}-52 \hat{j}$ are collinear if:

  • A
    $\beta=20$
  • B
    $\beta=40$
  • Correct answer
    C
    $\beta=-40$
  • D
    $\beta=26$

Solution

For collinear of given vectors $\begin{aligned} & \frac{-8-3}{40-60}=\frac{-52+8}{\beta-40} \\ & \Rightarrow \frac{-11}{-20}=\frac{-44}{\beta-40} \\ & \Rightarrow \beta-40=-80 \\ & \Rightarrow \beta=-40 \end{aligned}$

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

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