Hello I need help to explain the affect of the cross product without the its current symbolism, but for angular momentum. I can explain angular momentum in terms of the cross product of 3D space formulated like this: |r| |v| * sin(angler.v) e-perp to r and v Eq.1 (I can explain this to students: length of the "position" and "perpedicular velocity" vector, etc.) THEN, in Euclidean Space, this cross product is equivalent to: (ry*vz-rz*vy) e1 + (ry*vz-rz*vy) e2 +(ry*vz-rz*vy) e3 Eq. 2 And I can work out how E1 becomes E2 in Euclidean space. And I can teach the students how to compute the angular momentum of a particle moving in a plane, but about an axis perpendicular to the plane. HOWEVER: I also know that there is an easier way to construct the cross product that does not carry the baggage of non-associativity I take the first vector, r, and create a skew symmetric matrix out of its components. And multiply that matrix by the column components of v. Let me call this Eq. 3 Good: Now the question: How can I go from a PHYSICAL description of the angular momentum, BYPASS the toxic cross product and go right to the skew symmetric form of computing this affect? In other words, I am only able to go from E1 to E2 to E3 But I prefer to go from E1 direct to E3 In fact, I would really like to go direct and only to E3. In other words, how can I explain what this skew symmetric form of the first vector does to the second vector that is the EQUIVALENT of talking about lengths and perpedicularity, but IN THE CONTEXT OF CLASSICAL ANGULAR MOMENTUM? Maybe this is a silly question.