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JEE Main202126 Feb 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Consider the three planes P 1 : 3 x + 15 y + 21 z = 9 P 2 : x - 3 y - z = 5 , and P 3 : 2 x + 10 y + 14 z = 5 Then, which one of the following is true?

Options

  1. AP 2 and P 3 are parallel.
  2. BP 1 , P 2 and P 3 all are parallel.
  3. CP 1 and P 2 are parallel.
  4. DP 1 and P 3 are parallel.

Correct answer

D. P 1 and P 3 are parallel.

Step-by-step solution

P 1 : x + 5 y + 7 z = 3 P 2 : x - 3 y - z = 5 P 3 : x + 5 y + 7 z = 5 2 For P 1   &   P 3 ,   1 1 = 5 5 = 7 7 . So, P 1 and P 3 are parallel.

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