Question

A line drawn through $P$, parallel to line $L$, meet the plane $\pi$ at point $Q$, then co-ordinates of $Q$ is

• A. $(6,8,13)$
• B. $(6,-8,13)$
• C. $(-6,8,13)$
• D. $(6,8,-13)$

Answer 1

Answer: (B)

$(6,-8,13)$

Equation of the line through $P(1,2,3)$ and parallel to line $L=\frac{x-1}{1}=\frac{y-12}{-2}=\frac{z-7}{2}$ is given by,
$\frac{x-1}{1}=\frac{y-12}{-2}=\frac{z-7}{2}=\lambda$(say)
$\therefore$ general point $\left(Q\right)$ on the line is $x=2\lambda +1$, $y=-2\lambda +2$, $z=2\lambda +3$.

This point $Q(2\lambda +1,-2\lambda +2,2\lambda +3)$ lies on the plane $\pi$ whose equation is $x+y+z=11$
$\therefore$ $\lambda -2\lambda +2\lambda +1+2+3=11$
$\Rightarrow$ $\lambda =5$

$\Rightarrow$ co-ordinates of $Q$ are $Q(6,-8,13)$
Hence, (b) is correct answer.