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NDA 1 2024 Maths, question 55

Topic: Analytical geometry

Q55

A line through (1,−1,2)(1,-1,2) with direction ratios ⟨3,2,2⟩⟨3,2,2⟩ meets the plane x+2y+3z=18x+2y+3z=18. What is the point of intersection of line and plane ?

  1. (a) (4,4,1)(4,4,1)
  2. (b) (2,4,1)(2,4,1)
  3. (c) (4,1,4)(4,1,4)Correct answer
  4. (d) (3,4,7)(3,4,7)

Solution.

Answer: (c) (4,1,4)(4,1,4)

  1. Parametrise the line as x = 1 + 3t, y = −1 + 2t, z = 2 + 2t.
  2. In the plane equation this gives 5 + 13t = 18, hence t = 1.
  3. The intersection is (4, 1, 4).