 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/c/solution

Use

(0, 1, 1)

as an anchor. Two directions in the required plane are

u = (2, 0, 2), v = (4, 1, 0) .

(- 2, 8, 2)

n = (- 1, 4, 1)

n \cdot [(x, y, z) - (0, 1, 1)] = 0, - x + 4 y + z = 5.

Direct substitution verifies all three given points. The independent direction vectors ensure the plane is uniquely determined.

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