If a, b, and c are vectors, and α and β are scalars, the exterior product has the following properties:Antisymmetry: a∧b=−b∧a. In particular, a∧a=0.Distributivity (or linearity): a∧(αb+βc)=α(a∧b)+β(a∧c).Associativity: a∧(b∧c)=(a∧b)∧c, which we write as Scalar operation: α∧β=αβ and α∧a=a∧α=αa.