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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2016 · Mathematics · Three Dimensional Geometry

A plane P passes through the line of intersection of the planes 2...

A plane P passes through the line of intersection of the planes 2x−y+3z=2,x+y−z=12 \mathrm{x}-\mathrm{y}+3 \mathrm{z}=2, \mathrm{x}+\mathrm{y}-\mathrm{z}=1 and the point (1,0,1)(1,0,1). What is the equation of the plane P?

Options

  1. A2x + 5y – 2 = 0
  2. B5x + 2y – 5 = 0
  3. Cx + z – 2 = 0
  4. D2x – y – 2z = 0

Correct answer

B. 5x + 2y – 5 = 0

Step-by-step solution

Eq. of plane through two given planes is : (2x−y+3z−2)+λ(x+y−z−1)=0∵(2 x-y+3 z-2)+\lambda(x+y-z-1)=0\because It passes through (1,0,1)∴3−λ=0⇒λ=3∴(1,0,1)\therefore 3-\lambda=0 \Rightarrow \lambda=3\therefore Eq. of plane is: 5x+2y−5=05 x+2 y-5=0
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