Q85 / 150 · MHT CET 2023 (13 May Shift 1) · Mathematics

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

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

Solution

Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be the direction ratios of the required line. Since the line is perpendicular to the lines with d.r.s. $1,2,3$ and $-3,2,5$. $$ \begin{aligned} \therefore \quad & a+2 b+3 c=0 \\ & \text { and }-3 a+2 b+5 c=0 . \\ & \Rightarrow \frac{a}{2}=\frac{b}{-7}=\frac{c}{4} \end{aligned} $$ ....[From (i) and (ii)] $\therefore \quad$ Equation of the required line is $$ \frac{x+1}{2}=\frac{y-3}{-7}=\frac{z+2}{4} $$

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

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