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MHT CET202525 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

If the plane x 2 - y 3 - z 5 =1 cuts the co-ordinate axes in point A, B, C respectively, then the area of the triangle A B C is

Options

  1. A17 2 sq. units
  2. B19 2 sq. units
  3. C11 2 sq. units
  4. D15 2 sq. units

Correct answer

B. 19 2 sq. units

Step-by-step solution

The plane equation x 2 - y 3 - z 5 =1 is in intercept form with a=2 on the x-axis, b=-3 on the y-axis, and c=-5 on the z-axis, giving intercept points: A=(2,0,0) , B=(0,-3,0) , and C=(0,0,-5) . Compute vectors AB =(-2,-3,0) and AC =(-2,0,-5) . The cross product is 15 i - 10 j - 6 k with magnitude 19 . The triangle area is 1 2 19 = 19 2 square units.

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