Which one of the planes is parallel to the line \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}?
- A. x+2y+z-1=0
- B. 2x-y-2z+5=0
- C. 2x+2y-2z+1=0
- D. x-2y+z-1=0 ✓
Correct Answer: D. x-2y+z-1=0
Explanation
A line is parallel to a plane if its direction ratios (a, b, c) are perpendicular to the plane's normal direction ratios (A, B, C), meaning aA + bB + cC = 0. Here, (a, b, c) = (3, 4, 5). Checking the option x-2y+z-1=0, we evaluate 3(1) + 4(-2) + 5(1) = 3 - 8 + 5 = 0. Thus, this plane is parallel to the line.
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