 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-1/5b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The

i

th face through

v

contains the two edge directions

e_{j}

with

j \neq = i

, so

a_{i} \cdot e_{j} = 0

for those

j

. The one-dimensional space with these two orthogonality conditions is spanned by

f_{i}

, hence

a_{i} = λ_{i} f_{i}

for some nonzero real

λ_{i}

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