Q72 / 150 · MHT CET 2024 (10 May Shift 1) · Mathematics

If the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{-1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then k is equal to

  • Correct answer
    A
    $\frac{-5}{6}$
  • B
    $\frac{5}{6}$
  • C
    $\frac{6}{5}$
  • D
    $\frac{-6}{5}$

Solution

$\begin{aligned} & \therefore \quad\left|\begin{array}{ccc}x_2-x_1, & y_2-y_1, & z_2-z_i \\ \mathrm{a}_1 & \mathrm{~b}_1 & \mathrm{c}_1 \\ \mathrm{a}_2 & \mathrm{~b}_2 & \mathrm{c}_2\end{array}\right|=0 \\ & \therefore \quad\left|\begin{array}{ccc}3-1 & \mathrm{k}-2 & 0-1 \\ 2 & 3 & 4 \\ -1 & 2 & 1\end{array}\right|=0 \\ & \therefore \quad\left|\begin{array}{ccc}2 & \mathrm{k}-2 & -1 \\ 2 & 3 & 4 \\ -1 & 2 & 1\end{array}\right|=0 \\ & \therefore \quad \mathrm{k}=\frac{-5}{6}\end{aligned}$

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

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