If the image of the point P(1,−2,3) in the plane, 2x+3y−4z+22=0 measured parallel to the line, x1=y4=z5 is Q, then PQ is equal to

# If the image of the point $P\left(1,-2,3\right)$ 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

1. A

$2\sqrt{42}$

2. B

$\sqrt{42}$

3. C

$6\sqrt{5}$

4. D

$3\sqrt{5}$

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### Solution:

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

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

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

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

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