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JEE Main2013MathematicsThree Dimensional GeometryActual

If the lines x - 2 1 = y - 3 1 = z - 4 - k and x - 1 k = y - 4 2 = z - 5 1 are coplanar, then k can have

Options

  1. Aexactly two values.
  2. Bexactly three values.
  3. Cany value.
  4. Dexactly one value.

Correct answer

A. exactly two values.

Step-by-step solution

For 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 to be 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 . ∴ 1 - 1 - 1 1 1 - k k 2 1 = 0 ⇒ k = 0 ,   - 3 Hence, there are exactly two values of k .

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