Q83 / 180 · COMEDK 2024 (Memory Based) · Mathematics

If the lines $\frac{x+4}{3}=\frac{y-2}{a}=\frac{z}{2}$ and $\frac{x}{2}=\frac{y-3}{4}=\frac{z-1}{1}$ are perpendicular, then the value of $a$ is

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

Solution

Let $L_1 \equiv \frac{x+4}{3}=\frac{y-2}{a}=\frac{z}{2}$
$\therefore$ Direction ratio of $L_1\left(l_1, m_1, n_1\right)=(3, a, 2)$
$L_2 \equiv \frac{x}{2}=\frac{y-3}{4}=\frac{z-1}{1}$
$\therefore$ Direction ratio of $L_2\left(l_2, m_2, n_2\right)=(2,4,1)$
If given lines are perpendicular, then
$\begin{array}{ll} <br/>& l_1 l_2+m_1 m_2+n_1 n_2=0 \\<br/>\Rightarrow \quad & 3 \times 2+4 \times a+2 \times 1=0 \\<br/>\Rightarrow \quad & 4 a+8=0 \\<br/>\Rightarrow \quad & a=-2<br/>\end{array}$

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

Relevant Questions