1. Compute meet and join of two vectors a and b in general position, and show that the magnitude of their meet (relative to their join) is the sine of their angle. Relate the sign of the sine to the order of intersection. In this case, the meet should be antisymmetric.
2. As an exercise in symbolic manipulation of the products so far, let us consider the meet of a ∧ B and a ∧ C, where a is a vector and the blades B and C have no common factor. The answer should obviously be proportional to a, but what precisely is the proportionality factor? (Hint: If you get stuck, the next exercise derives the answer as (a ∧ B ∧ C)∗.)