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JEE Main202116 Mar 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Let P be a plane l x + m y + n z = 0 containing the line, 1 - x 1 = y + 4 2 = z + 2 3 . If plane P divides the line segment A B joining points A - 3 , - 6 , 1 and B 2 , 4 , - 3 in ratio k : 1 then the value of k is equal to :

Options

  1. A1 . 5
  2. B3
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

Point C is 2 k - 3 k + 1 , 4 k - 6 k + 1 , - 3 k + 1 k + 1 x - 1 - 1 = y + 4 2 = z + 2 3 Plane l x + m y + n z = 0 l - 1 + m 2 + n 3 = 0 - l + 2 m + 3 n = 0 . . . ( 1 ) It also satisfy point 1 , - 4 , - 2 l - 4 m - 2 n = 0 . . . ( 2 ) Solving ( 1 ) and ( 2 ) 2 m + 3 n = 4 m + 2 n n = 2 m l - 4 m - 4 m = 0 l = 8   m l 8 = m 1 = n 2 l : m : n = 8 : 1 : 2 Plane is 8 x + y + 2 z = 0 It will satisfy point C 8 2 k - 3 k + 1 + 4 k - 6 k + 1 + 2 - 3 k + 1 k + 1 = 0 16 k - 24 + 4 k - 6 - 6 k + 2 = 0 14 k = 28  &#1

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