If the image of the point $P(1,-2,3)$ in the plane, $2x+3y-4z+22=0$ measured parallel to the line, $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is Q, then PQ is equal to

Equation of the line passing through $P(1,-2,3)$

with dr's (1,4,5) is $\frac{x-1}{1}=\frac{y+2}{4}=\frac{z-3}{5}=t$

$R(t+1,4t-2,5t+3)$ lies on the plane then t = 1    ,R (2,2,8)

$PQ=2PR=2\sqrt{1+16+25}=2\sqrt{42}$