JEE Math Practice Question

Let the image of the point $$(1,0,7)$$ in the line $$\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$$ be the point $$(\alpha, \beta, \gamma)$$. Then which one of the following points lies on the line passing through $$(\alpha, \beta, \gamma)$$ and making angles $$\frac{2 \pi}{3}$$ and $$\frac{3 \pi}{4}$$ with $$y$$-axis and $$z$$-axis respectively and an acute angle with $$x$$-axis ?

1. A.$$(1,-2,1+\sqrt{2})$$
2. B.$$(3,-4,3+2 \sqrt{2})$$
3. C.$$(3,4,3-2 \sqrt{2})$$
4. D.$$(1,2,1-\sqrt{2})$$