Q74 / 150 · MHT CET 2024 (11 May Shift 1) · Mathematics

If the lines $\frac{x+1}{-10}=\frac{y+\mathrm{k}}{-1}=\frac{z-4}{1}$ and $\frac{x+10}{-1}=\frac{y+1}{-3}=\frac{z-1}{4}$ intersect each other, then the value of $k$ is

  • A
    -3
  • Correct answer
    B
    3
  • C
    4
  • D
    2

Solution

Since the given lines intersect, $\begin{aligned} & \left|\begin{array}{ccc} x_2-x_1 & y_2-y_1 & z_2-z_1 \\ a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \end{array}\right|=0 \\ & \left|\begin{array}{ccc} -10+1 & -1+\mathrm{k} & 1-4 \\ -10 & -1 & 1 \\ -1 & -3 & 4 \end{array}\right|=0 \\ & \Rightarrow\left|\begin{array}{ccc} -9 & -1+\mathrm{k} & -3 \\ -10 & -1 & 1 \\ -1 & -3 & 4 \end{array}\right|=0 \\ & \Rightarrow 39 \mathrm{k}=117 \\ & \Rightarrow \mathrm{k}=3 \end{aligned}$

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

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