Q82 / 125 · BITSAT 2011 · Mathematics

Gives the line \(L: \frac{x-1}{3}=\frac{y+1}{2}=\frac{z-3}{-1}\) and the plane \(\pi: x-2 y-z=0\). Of the following assertions, the only one that is always true is

  • A
    L is \(\perp\) to \(\pi\)
  • Correct answer
    B
    L lies in \(\pi\)
  • C
    L is not parallel to \(\pi\)
  • D
    None of these

Solution

Since \(3(1)+2(-2)+(-1)(-1)=3-4+1=0\) \(\therefore\) Given line is \(\perp\) to the normal to the plane i.e., given line is parallel to the given plane. Also, \((1,-1,3)\) lies on the plane \(x-2 y-z=0\) if \(1-2(-1)-3=0\) i.e., \(1+2-3=0\) which is true \(\therefore\) L lies in plane \(\pi\).

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

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