 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/3/a/solution

Adding the vectors component by component gives

u + v = (5 a, 0, 2 a)^{T} = 0 .

Consequently

a = 0

. The requirement that the vectors be nonzero then implies

b \neq = 0

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