As near as I can figure it:
(a⊗b)∧c = a⊗b⊗c - a⊗c⊗b + c⊗a⊗b
But I'm not sure if thats right.
a, b, and c are vectors.
I know that a∧b = a⊗b - b⊗a which is a bivector.
The equation I am most interested in is a∧b∧c = (a⊗b - b⊗a)∧c which is evidently a trivector and a rank 3 tensor. I know that the wedge product distributes over addition.