Key properties: (1) a x a = 0 for any vector. (2) Anti-commutative: a x b = -b x a. (3) Distributive: a x (b + c) = a x b + a x c. (4) NOT associative: a x (b x c) != (a x b) x c in general. (5) k(a x b) = (ka) x b = a x (kb). Geometric applications: Area of parallelogram with sides a, b = |a x b|. Area of triangle = $\frac{1}{2}$|a x b|. Two non-zero vectors are parallel iff a x b = 0. A unit vector perpendicular to both a and b is (a x b)/|a x b|.