 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/9/a/solution

Contracting the Kronecker delta identifies

i = k

. The remaining two independent sums are dot products, so the Einstein summation convention gives

a_{i} δ_{ik} b_{m} a_{m} c_{k} = (\sum_{k} a_{k} c_{k}) (\sum_{m} b_{m} a_{m}) = (a \cdot c) (a \cdot b) .

The index expression here is verified against the PDF because the OCR corrupts it completely.

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