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 $\frac{x-2}{1} = \frac{y-3}{-2} = \frac{z-4}{5}$