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JEE Main202227 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

If two straight lines whose direction cosines are given by the relations l + m - n = 0 , 3 l 2 + m 2 + c n l = 0 are parallel, then the positive value of c is

Options

  1. A6
  2. B4
  3. C3
  4. D2

Correct answer

A. 6

Step-by-step solution

Given, l + m - n = 0 & 3 l 2 + m 2 + c l n = 0 Now taking n = l + m and putting in 3 l 2 + m 2 + c l n = 0 we get, 3 l 2 + m 2 + c l l + m = 0 ⇒ 3 l 2 + m 2 + c l 2 + c l m = 0 ⇒ 3 + c l 2 + c l m + m 2 = 0 ⇒ 3 + c l m 2 + c l m + 1 = 0 ..equation (i) ∵ lies are parallel. So, roots of equation (i) must be equal ⇒   D = 0 ⇒ c 2 - 4 3 + c = 0 ⇒ c 2 - 4 c - 12 = 0 ⇒ c - 6 c + 2 = 0 c = 6 or c = - 2 So, positive value of c = 6

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