 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/14/d/solution

The axis intercepts of the plane are

P = (- 5, 0, 0), Q = (0, 5/4, 0), R = (0, 0, 5) .

Use two edge vectors from

P

(Q - P) \times (R - P) = (5, 5/4, 0) \times (5, 0, 5) = (25/4, - 25, - 25/4) .

The triangle area is half this cross product magnitude:

A = \frac{1}{2} \frac{25}{4} 1 + 16 + 1 = \frac{75 2}{8} .

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