Let the image of the point \( (1,0,7) \) in the line \(\displaystyle \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) 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 \(\displaystyle \frac{2\pi}{3} \) and \(\displaystyle \frac{3\pi}{4} \) with \( y \)-axis and \( z \)-axis respectively and an acute angle with \( x \)-axis?
