Question

If Q is the image of the point P(2, 3, 4) under the reflection in the plane x - 2y + 5z = 6, then the equation of the line PQ is

• A. $\frac{x-2}{-1}=\frac{y-3}{2}=\frac{z-4}{5}$
• B. $\frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-4}{5}$
• C. $\frac{x-2}{-1}=\frac{y-3}{-2}=\frac{z-4}{5}$
• D. $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{5}$

Answer 1

Answer: (B)

Let Q be the image of the point $P(2,3,4)$ in the plane $x-2y+5z=6$, then PQ is normal to the plane
$\therefore$ direction ratios of PQ are $<1,-2,5>$
Since PQ passes through $P\left(2,3,4\right)$ and has direction ratios $1,-2,5$
$\therefore$ Equation of PQ is $\frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-4}{5}$