Q80 / 150 · MHT CET 2024 (11 May Shift 1) · Mathematics

The equation of the line passing through the point $(3,1,2)$ and perpendicular to the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$ is

  • A
    $\frac{x+3}{2}=\frac{y+1}{7}=\frac{z+2}{4}$
  • B
    $\frac{x-3}{-2}=\frac{y-1}{7}=\frac{z-2}{4}$
  • Correct answer
    C
    $\frac{x-3}{2}=\frac{y-1}{-7}=\frac{z-2}{4}$
  • D
    $\frac{x-3}{2}=\frac{y-1}{5}=\frac{z-2}{4}$

Solution

Required line is perpendicular to the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$. $\therefore \quad$ Required line is parallel to vector $\bar{b}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & 3 \\ -3 & 2 & 5\end{array}\right|$ $=4 \hat{i}-14 \hat{j}+8 \hat{k}$ $\therefore \quad$ The equation of the required line is $\frac{x-3}{2}=\frac{y-1}{-7}=\frac{z-2}{4}$

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

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