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MHT CET202615 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

The co-ordinates of the point where the line joining the points (3,5,-7) and (-2, 1, 8) is intersected by the YOZ plane are

Options

  1. A(0, -13 5 , 2 5 )
  2. B(0, 13 5 , 2 5 )
  3. C(0, 13 5 , 2 )
  4. D(0, -13 5 , -2 )

Correct answer

C. (0, 13 5 , 2 )

Step-by-step solution

The equation of the line joining the points (3, 5, -7) and (-2, 1, 8) is given by x - 3 -2 - 3 = y - 5 1 - 5 = z - (-7) 8 - (-7) x - 3 -5 = y - 5 -4 = z + 7 15 = k Any point on this line is of the form (-5k + 3, -4k + 5, 15k - 7) . The line intersects the YOZ plane, where the x-coordinate is zero. -5k + 3 = 0 k = 3 5 Substituting k = 3 5 in the y and z coordinates, we get y = -4 ( 3 5 ) + 5 = -12 + 25 5 = 13 5 z = 15 ( 3 5 ) - 7 = 9 - 7 = 2 The required coordinates are (0, 13 5 , 2 ) . Answer: (0, 13 5 , 2 )

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