Interchange the two dummy indices $j,k$. The product $a_ja_k$ is symmetric under this interchange, while the <Levi-Civita symbol> changes sign. Thus the contraction equals its negative and is \b[the zero <vector>], equivalently $\mathbf a\times\mathbf a=\mathbf0$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / ia / Paper 1 / 1C / v / Solution

 Solution (source code)