 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/11/a/iii/solution

O A = a e + b f + c g

\frac{b + c}{2} = 1, \frac{a + c}{2} = 0, \frac{a + b}{2} = 0.

The unique solution, guaranteed by the basis property, is

(a, b, c) = (- 1, 1, 1)

. Thus

O A = - e + f + g .

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