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JEE Main202313 Apr 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The line, that is coplanar to the line x + 3 - 3 = y - 1 1 = z - 5 5 , is

Options

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

Correct answer

B. x + 1 - 1 = y - 2 2 = z - 5 5

Step-by-step solution

We know that two lines x - x 1 a 1 = y - y 1 b 1 = z - z 1 c 1 and x - x 2 a 2 = y - y 2 b 2 = z - z 2 c 2 are coplanar if x 2 - x 1 y 2 - y 1 z 2 - z 1 a 1 b 1 c 1 a 2 b 2 c 2 = 0 Let us verify this option. The given lines are x + 3 - 3 = y - 1 1 = z - 5 5 and x + 1 - 1 = y - 2 2 = z - 5 5 . = - 1 - - 3 2 - 1 5 - 5 - 3 1 5 - 1 2 5 = 2 1 0 - 3 1 5 - 1 2 5 = 2 5 - 10 - 1 - 15 - - 5 + 0 = 2 - 5 + 10 = 0 Therefore, this is the correct option.

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