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JEE Main2015MathematicsThree Dimensional GeometryActual

The shortest distance between the z - axis and the line x + y + 2 z - 3 = 0 = 2 x + 3 y + 4 z - 4 , is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

We have, x + y + 2 z - 3 = 0 = 2 x + 3 y + 4 z - 4 Change it into symmetrical form Put z = 1 , then x + y - 1 = 0 2 x + 3 y = 0 On solving, we get x = 3 ,   y = - 2 ,   z = 1 3 ,   - 2   ,   1 Direction ratio of the line is = i ^ j ^ k ^ 1 1 2 2 3 4 = - 2 i ^ + k ^ Hence, equation of line in symmetrical form is x - 3 - 2 =   y + 2 0 = z - 1 1 Equation of z axis is, x 0 =   y 0 =   z 1   Shortest Distance = 3 - 2 1 - 2 0 1 0 0 1 i ^ j ^ k ^ - 2 0 1 0 0 1 = - 4 2 j ^ = 2

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