Q135 / 200 · Manipal (MET) 2014 · Mathematics

A perpendicular is drawn from the point $P(2,4,-1)$ to the line $\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}$. The equation of the perpendicular from $P$ to the given line is

  • Correct answer
    A
    $\frac{x-2}{6}=\frac{y-4}{3}=\frac{z+1}{2}$
  • B
    $\frac{x+2}{6}=\frac{y-4}{3}=\frac{z+1}{2}$
  • C
    $\frac{x+2}{-6}=\frac{y-4}{3}=\frac{z+1}{2}$
  • D
    $\frac{x+2}{6}=\frac{y+4}{3}=\frac{z+1}{2}$

Solution

Obtain the foot of the perpendicular $N(-4,1,-3)$. Find the equations of the line passing through $\begin{aligned} & P(2,4,-1) \text { and } N(-4,1,-3) \\ & \qquad \frac{x-2}{6}=\frac{y-4}{3}=\frac{z+1}{2} \end{aligned}$

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

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