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NDA 2 2024 Maths, question 69

Topic: Analytical geometry

Passage · Q69 to Q70

Let L:x+y+z+4=0=2x−y−z+8L:x+y+z+4=0=2x-y-z+8 be a line and P:x+2y+3z+1=0P:x+2y+3z+1=0 be a plane.

Q69

What are the direction ratios of the line?

  1. (a) ⟨2,1,−1⟩⟨2,1,-1⟩
  2. (b) ⟨0,−1,2⟩⟨0,-1,2⟩
  3. (c) ⟨0,1,−1⟩⟨0,1,-1⟩Correct answer
  4. (d) ⟨2,3,−3⟩⟨2,3,-3⟩

Solution.

Answer: (c) ⟨0,1,−1⟩⟨0,1,-1⟩

  1. The two normals are (1,1,1) and (2,−1,−1).
  2. Their cross product is (0,3,−3), proportional to (0,1,−1).
  3. This direction is perpendicular to both normals, as required.