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Let the image of the point "(1,0,7)" in ...

Let the image of the point `"(1,0,7)"` in the line `(x)/(1)=(y-1)/(2)=(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 `(2 pi)/(3)` and `(3 pi)/(4)` with "y" -axis and `"z" `-axis respectively and an acute angle with` "x"` -axis ?

A

`(3,-4,3+2sqrt(2))`

B

`(1,-2,1+sqrt(2))`

C

`(3,4,3-2sqrt(2))`

D

`(1,2,1-sqrt(2))`

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