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NDA 1 2024 Maths, question 56

Topic: Analytical geometry

Q56

If pp is the perpendicular distance from origin to the plane passing through (1,0,0)(1,0,0), (0,1,0)(0,1,0) and (0,0,1)(0,0,1), then what is 3p23p^{2} equal to ?

  1. (a) 44
  2. (b) 33
  3. (c) 22
  4. (d) 11Correct answer

Solution.

Answer: (d) 11

  1. The intercept form gives the plane x + y + z = 1.
  2. Its perpendicular distance from the origin is p = 1/√3.
  3. Consequently 3p² = 1.