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JEE Main202228 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

Let the lines x - 1 λ = y - 2 1 = z - 3 2 and x + 26 - 2 = y + 18 3 = z + 28 λ be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lies on P ?

Options

  1. A0 , - 2 , - 2
  2. B- 5 , 0 , - 1
  3. C3 , - 1 , 0
  4. D0 , 4 , 5

Correct answer

D. 0 , 4 , 5

Step-by-step solution

Given, L 1 : x - 1 λ = y - 2 1 = z - 3 2 and L 2 : x + 26 - 2 = y + 18 3 = z + 28 λ are coplanar Now using the condition of coplanarity we get, ⇒ 27 20 31 λ 1 2 - 2 3 λ = 0 ⇒ λ = 3 Now, normal of plane P , which contains L 1 and L 2 is given by i ^ j ^ k ^ 3 1 2 - 2 3 3 = - 3 i ^ - 13 j ^ + 11 k ^ Now equation of required plane P will be - 3 x - 1 - 13 y - 2 + 11 z - 3 = 0 ⇒ 3 x + 13 y - 11 z + 4 = 0 Now satisfy all given points from option we get, 0 , 4 , 5 does not lie o

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