 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/ia/paper-1/7b/i/a/solution

u \cdot v = 0

, use the positively oriented orthonormal basis

(u, v \times u, v)

. The cross product identities give

A u = u + v \times u

A (v \times u) = - u

and

A v = 0

. In this basis,

A = 110 - 1 00 000 .

λ (λ^{2} - λ + 1)

, so

λ = 0, \frac{1 + i 3}{2}, \frac{1 - i 3}{2} .

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