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  4. Consider the line L given by the equation (x-3/2)=(y-1/1)=(z-2/1). Let Q be the mirror image of the point (2,3,-1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?

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Q. Consider the line $L$ given by the equation $\frac{x-3}{2}=\frac{y-1}{1}=\frac{z-2}{1}$. Let $Q$ be the mirror image of the point $(2,3,-1)$ with respect to $L$. Let a plane $P$ be such that it passes through $Q$, and the line $L$ is perpendicular to $P$. Then which of the following points is on the plane $P$ ?

JEE MainJEE Main 2021Three Dimensional Geometry

Solution:

Plane mathrm $p$ is $\perp^{r}$ to line
$\frac{x-3}{2}=\frac{y-1}{1}=\frac{z-2}{1}$
\& passes through pt. $(2,3)$ equation of plane $p$
$2(x-2)+1(y-3)+1(z+1)=0$
$2 x+y+z-6=0$
pt $(1,2,2)$ satisfies above equation