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

The correct option is B
2√42
Equation of plane:P
2x+3y-z+22=0
Direction ratio of plane are:(2,3,-1)
Equation of line:L
x/1=y/4=z/5
Direction ratio of line are:(1,4,5)
Equation of a line PQ passing through point P(1,-2,3) along line L is:
x-1/1=y+2/4=z-3/5=k
=>x=k+1,y=4k-2,z=5k+3
Lets say R is the mid point of the line PQ, therefore R lie on the plane.
Hence, it should satisfy the equation of the plane.
2(k+1)+3(4k-2)-(5k+3)+22=0
=>k=1
Coordinates of R=(2,2,8)
Length of the image PQ=2PR
=>PQ=2√(2-1)²+(2+2)²+(8-3)²=2√42