1. The problem statement, all variables and given/known data This is my first exposure to Einstein notation and I'm not sure if I'm understanding it entirely. Also I added this class after my instructor had already lectured about the topic and largely had to teach myself, so I ask for your patience in advance... The question is: Evaluate the following expression: εijkaiaj 2. Relevant equations a ^ b = ai ei ^ bj ej = aibj (ei ^ ei) = aibj εijk ek Where I'm following his notation that ^ represents the cross product of the two vectors 3. The attempt at a solution Now, just going off what I have seen so far in the handout he has posted, I believe the answer to be εijkaiaj = (a ^ a)k or, εijkaiaj is the kth component of a ^ b and because the expression is a vector crossed with itself it is equal to zero But what does it mean to be the kth component of a cross product? Honestly I'm working backward from a similar to an example he has in the handout and making the assumption that the reason the ek component is absent from the expression is because it is the kth component of the cross product, but from what I have to reference I cannot say with any degree of certainty if that is true and it makes me uncomfortable. Any help is greatly appreciated.