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NDA 2 2025 Maths, question 51

Topic: Analytical geometry

Passage · Q51 to Q52

A plane PP is parallel to the line having direction ratios ⟨1,3,2⟩⟨1,3,2⟩ and contains the line of intersection of the planes 6x+4y−5z=26x+4y-5z=2 and x−2y+3z=0x-2y+3z=0.

Q51

Which of the following are the direction ratios of the line of intersection of the given planes?

  1. (a) ⟨2,23,16⟩⟨2,23,16⟩
  2. (b) ⟨2,−23,−16⟩⟨2,-23,-16⟩Correct answer
  3. (c) ⟨2,3,2⟩⟨2,3,2⟩
  4. (d) ⟨−1,3,−2⟩⟨-1,3,-2⟩

Solution.

Answer: (b) ⟨2,−23,−16⟩⟨2,-23,-16⟩

  1. The line of intersection is perpendicular to both plane normals.
  2. Their cross product is (6,4,−5)×(1,−2,3)=(2,−23,−16).
  3. Its dot products with both normals are zero, confirming option (b).