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Lets do a little compare and contrast between the dot product and the cross product. Let me just make two vectors-- just visually draw them. And maybe if we have time, well, actually figure out some dot and cross products with real vectors. Lets call the first one-- Thats the angle between them. OK. So lets just go over the definitions and then well work on the intuition. And hopefully, you have a little bit of both already. So what is a dot b? Well first of all, thats the exact same thing as b dot a. Order does not matter when you take the dot product because you end up with just a number. And that is equal to the magnitude of a times the magnitude of b times cosine of the angle between them. Lets look at the definition of the cross product. What is a cross b? Well first of all, that does not equal b cross a. It actually equals the opposite direction, or you could view it as the negative of b cross a. Because the vector that you end up with ends up flipped, whichever order you
