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MHT CET202618 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The line passes through the point (2, 1, 1) and is parallel to the plane x + y + 2z = 18 . If line intersects the line x+2 3 = y+1 -1 = z-2 1 , then equation of the line is...

Options

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

Correct answer

D. x-3 1 = y-4 3 = z+1 -2

Step-by-step solution

Let the point of intersection of line and the given line be Q . Any point on the given line x+2 3 = y+1 -1 = z-2 1 = can be written as Q(3 - 2, - - 1, + 2) . The line passes through P(2, 1, 1) and Q . The direction ratios of are proportional to the vector PQ : PQ = (3 - 2 - 2) i + (- - 1 - 1) j + ( + 2 - 1) k PQ = (3 - 4) i + (- - 2) j + ( + 1) k Since the line is parallel to the plane x + y + 2z = 18 , it is perpendicular to the normal vector of the plane, n = i + j + 2 k . Therefore, PQ n = 0 : 1(3 - 4) + 1(- - 2

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