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MHT CET202520 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The co-ordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) and intersects the plane 2 x+y+z=7 are

Options

  1. A(-1,2,7)
  2. B(1,2,3)
  3. C(2,1,2)
  4. D(1,-2,7)

Correct answer

D. (1,-2,7)

Step-by-step solution

Given points P₁(2,-3,1) and P₂(3,-4,-5) , the direction vector of the line is d = (1,-1,-6) . The parametric equations of the line through P₁ are: x = 2 + t y = -3 - t z = 1 - 6t Substituting into the plane equation 2x + y + z = 7 gives: 2(2+t) + (-3-t) + (1-6t) = 7 Simplifying: 4 + 2t - 3 - t + 1 - 6t = 7 2 - 5t = 7 t = -1 Substituting t = -1 back into the parametric equations yields the intersection point (1, -2, 7) , which corresponds to option D. The correct answer is D .

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