Q48 / 120 · JEE Main 2007 · Mathematics

Let $L$ be the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If $L$ makes an angles $\alpha$ with the positive $x$-axis, then $\cos \alpha$ equals

  • Correct answer
    A
    $\frac{1}{\sqrt{3}}$
  • B
    $\frac{1}{2}$
  • C
    $1$
  • D
    $\frac{1}{\sqrt{2}}$

Solution

If direction cosines of $L$ be $l$, $m, n$, then $\begin{aligned} & 2 l+3 m+n=0 \\ & l+3 m+2 n=0 \end{aligned}$ Solving, we get, $\frac{l}{3}=\frac{m}{-3}=\frac{n}{3}$ $\therefore l: m: n=\frac{1}{\sqrt{3}}:-\frac{1}{\sqrt{3}}: \frac{1}{\sqrt{3}} \Rightarrow \cos \alpha=\frac{1}{\sqrt{3}} \text {. }$

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

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