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NDA 2 2024 Maths, question 67

Topic: Analytical geometry

Passage · Q67 to Q68

Let SS be the line of intersection of two planes x+y+z=1x+y+z=1 and 2x+3y−4z=82x+3y-4z=8.

Q67

Which of the following are the direction ratios of SS?

  1. (a) ⟨−7,−6,1⟩⟨-7,-6,1⟩
  2. (b) ⟨−7,6,1⟩⟨-7,6,1⟩Correct answer
  3. (c) ⟨−6,5,1⟩⟨-6,5,1⟩
  4. (d) ⟨6,5,1⟩⟨6,5,1⟩

Solution.

Answer: (b) ⟨−7,6,1⟩⟨-7,6,1⟩

  1. The line's direction is perpendicular to both plane normals (1,1,1) and (2,3,−4).
  2. Their cross product is (−7,6,1).
  3. Its dot products with the normals are −7+6+1=0 and −14+18−4=0, confirming (b).