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MHT CET202520 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

If the plane x 3 + y 2 - z 4 =1 cuts the co-ordinate axes at points A , B and C , then the area of the triangle A B C is

Options

  1. A61 2 sq. units
  2. B2 61 sq. units
  3. C61 sq. units
  4. D3 61 sq. units

Correct answer

C. 61 sq. units

Step-by-step solution

The plane equation x 3 + y 2 - z 4 = 1 is in intercept form, yielding intercepts at (3, 0, 0) , (0, 2, 0) , and (0, 0, -4) . The vectors AB = (-3, 2, 0) and AC = (-3, 0, -4) represent two sides of triangle ABC . The cross product is AB AC = (-8, -12, 6) , with magnitude | AB AC | = 64 + 144 + 36 = 244 = 2 61 . The area is 1 2 2 61 = 61 square units. Answer: C

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