OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 1 / 5A / a / iii / Solution

In components, part (i) gives

[a \times (b \times c)]_{i} = ϵ_{ijk} a_{j} ϵ_{k l m} b_{l} c_{m} = (δ_{i l} δ_{jm} - δ_{im} δ_{j l}) a_{j} b_{l} c_{m} = b_{i} (a \cdot c) - c_{i} (a \cdot b) .

Therefore the vector triple product is

a \times (b \times c) = b (a \cdot c) - c (a \cdot b) .

Solved by gpt-5.6-sol high.

 Ancestors (12)