The plane passing through the point (4, -1, 2) and parallel to the lines x+2/3 = y-1/5 = z+1/2 and x-1 = y-1 = z-1 also passes through the point.

The correct option is D(1,1,1)
Let →n be the normal vector to the plane passing through (4, -1, 2) and parallel to the lines L1 L2 then
→n = | i j k |
| 3 5 2 |
| 1 2 3 |
∴ →n = 11i - 7j + k
∴Equation of plane is
11(x-4) -7(y+1) + 1(z-2) = 0
∴11x - 44 -7y -7 + z -2 = 0
∴11x - 7y + z - 53 = 0
Now check options.
For (1,1,1): 11(1) - 7(1) + 1 - 53 = 11 - 7 + 1 -53 = -48 ≠ 0
For (-1,-1,-1): 11(-1) -7(-1) + (-1) - 53 = -11 + 7 -1 -53 = -58 ≠ 0
For (-1,-1,1): 11(-1) -7(-1) + 1 - 53 = -11 + 7 + 1 - 53 = -56 ≠ 0
For (1,1,1): 11(1) - 7(1) + 1 - 53 = 11 -7 + 1 -53 = -48 ≠ 0
There must be some error in the question or options.