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MHT CET2018MathematicsThree Dimensional Geometry

The equation of line passing through ( 3 , − 1 , 2 ) and perpendicular to the lines r → = ( i ^ + j ^ − k ^ ) + λ ( 2 i ^ − 2 j ^ + k ^ ) and r → = ( 2 i ^ + j ^ − 3 k ^ ) + μ ( i ^ − 2 j ^ + 2 k ^ ) is

Options

  1. Ax + 3 2 = y + 1 3 = z - 2 2
  2. Bx - 3 3 = y + 1 2 = z - 2 2
  3. Cx - 3 2 = y + 1 3 = z - 2 2
  4. Dx - 3 2 = y + 1 2 = z - 2 3

Correct answer

C. x - 3 2 = y + 1 3 = z - 2 2

Step-by-step solution

A vector perpendicular to given lines is ∴ | i ^ j ^ k ^ 2 − 2 1 1 − 2 2 | = − 2 i ^ − 3 j ^ − 2 k ^ ∴ drs of line a = − 2, b = − 3, c = − 2, Or a = 2, b = 3, c = 2, Equation of line is x − 3 2 = y + 1 3 = z − 2 2

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