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JEE Main2017MathematicsThree Dimensional GeometryActual

The line of intersection of the planes r → ⋅ 3 i ^ - j ^ + k ^ = 1 and r → ⋅ i ^ + 4 j ^ - 2 k ^ = 2 , is,

Options

  1. Ax - 6 13 2 = y - 5 13 7 = z - 13
  2. Bx - 4 7 2 = y - 7 = z + 5 7 13
  3. Cx - 6 13 2 = y - 5 13 - 7 = z - 13
  4. Dx - 4 7 - 2 = y 7 = z - 5 7 13

Correct answer

C. x - 6 13 2 = y - 5 13 - 7 = z - 13

Step-by-step solution

n → =   n → 1 × n → 2   = i ^ j ^ k ^ 3 - 1 1 1 4 - 2 =   i ^   - 2 - j ^ - 7 + k ^ 13 n → = -2 i + 7 j ^ + 13 k ^ Now equations of plane are 3 x - y + z = 1 and x + 4 y - 2 z = 2 Let, z = 0 ⇒   3 x - y = 1 ⇒   x + 4 y = 2 ⇒   13 x = 6 x = 6 13 and y = 5 13 ∴ Equation of required line is, x - 6 13 - 2 = y - 5 13 7 = z - 0 13 or x - 6 13 2 = y - 5 13 - 7 = z - 13

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