Let $$(\alpha, \beta, \gamma)$$ be mirror image of the point $$(2, 3, 5)$$ in the line $$\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$$. Then $$2\alpha + 3\beta + 4\gamma$$ is equal to

Mirror image of (2,3,5) in line (x-1)/2=(y-2)/3=(z-3)/4.

Foot of perpendicular: point on line (1+2t,2+3t,3+4t). Direction to P: (1-2t,1-3t,2-4t)⊥(2,3,4).

2(1-2t)+3(1-3t)+4(2-4t)=0. 2-4t+3-9t+8-16t=0. 13-29t=0. t=13/29.

Foot=(1+26/29,2+39/29,3+52/29)=(55/29,97/29,139/29).

Mirror: α=2(55/29)-2=110/29-58/29=52/29. β=2(97/29)-3=194/29-87/29=107/29. γ=2(139/29)-5=278/29-145/29=133/29.

2α+3β+4γ=104/29+321/29+532/29=957/29=33.

The answer is Option (2): 33.