Prove that for vectors A,B and C, A.(B+C)=A.B+A.C and prove the property that for two vectors, A and B the dot product is equal to A^ie_i . B^je_j = e_i.e_jA^iB^j
Only use the definition where for two vectors a and b the (length of a)(length of b)cost =a.b
Generalize for an arbitrary coordinate system (not necessarily cartesian). Moreover, I'm not allowed to assume that the basis are the standard, I,j,k basis vectors. So the metric tensor is not the kronecker delta. I mean that I shouldn't assume that I'm just working in cartesian coordinates.
The Attempt at a Solution
For the first, I got length of A length ofB+C cost but I'm not sure what to do after that.