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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

Which one of the planes is parallel to the line...

Which one of the planes is parallel to the line \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?

Options

  1. A2x+2y+z−1=02 x+2 y+z-1=0
  2. B2x−y−2z+5=02 x-y-2 z+5=0
  3. C2x+2y−2z+1=02 x+2 y-2 z+1=0
  4. Dx−2y+z−1=0x-2 y+z-1=0

Correct answer

D. x−2y+z−1=0x-2 y+z-1=0

Step-by-step solution

If a line parallel to a plane then a1a2+b1b2+c1c2=0a_1 a_2+b_1 b_2+c_1 c_2=0 so option (A), 3.2+2.4+1.5≠03.2+2.4+1.5 \neq 0 (B) 2.3−1.4−2.5≠02.3-1.4-2.5 \neq 0 (C) 2.3+2.4−2.5≠02.3+2.4-2.5 \neq 0 (D) 1.3−2.4+1.5=01.3-2.4+1.5=0
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