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MHT CET202615 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

For the line x+1 1 = y-2 2 = z+3 3 , identify the incorrect statement among the following.

Options

  1. AIt can be represented by equation x+2 1 = y 2 = z+6 3
  2. BIt lies in the plane x - 2y + z + 8 = 0
  3. CIt is perpendicular to the plane x - 2y + z = 0
  4. DIt passes through point (0, 4, 0) .

Correct answer

C. It is perpendicular to the plane x - 2y + z = 0

Step-by-step solution

The given line is x+1 1 = y-2 2 = z+3 3 = . Any point on the line is of the form ( - 1, 2 + 2, 3 - 3) . For = -1 , the point is (-2, 0, -6) . Since the direction ratios remain the same, the line can be represented as x+2 1 = y 2 = z+6 3 . Thus, the first statement is correct. Substituting the general point into the plane x - 2y + z + 8 = 0 , we get ( - 1) - 2(2 + 2) + (3 - 3) + 8 = - 1 - 4 - 4 + 3 - 3 + 8 = 0 , which is true for all . Thus, the line lies in the plane, making the second statement correct. For = 1 ,

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