‫Welcome back.
‫Now that we have covered the DOT product, let's talk about the cross product.
‫Now, when we talk about cross products, then what you need to know is that the result of a cross product
‫is a vector and not scalar in this vector is not any kind of vector.
‫If you cross two vectors, let's say the one vector, cross the two vector, then the resulting vector
‫is perpendicular to both of these vectors.
‫For example, if the one and two are both on the x y plane, then the resulting vector would be either
‫in the positive or negative, the Z direction.
‫So here's an example.
‫I have three inertia frames here and you can see that the mesh here is the X Y plane.
‫So I put the one vector here, I put V to Vector here.
‫Both of them are on the X Y plane and the resulting vector will be in the Z direction like this in this
‫vectors perpendicular to this one and to this one.
‫Or if my V one vector vectors like this in my V two vectors like this, then that would be the resulting
‫vector in the negative Z direction.
‫Or if my V one vector is like this and my V two vectors like this, then that would be my result.
‫Note that the more parallel V one and the two are, the smaller the cross product result is in magnitude
‫and the more perpendicular they are, the bigger their answer is in magnitude.
‫Why is it like that?
‫Well, that is because when you have V one cross the two, then you only take that component of V two
‫that is perpendicular to V one, and then you multiply V one by this perpendicular component of V to
‫this component that is perpendicular to V one.
‫And so you multiply their magnitudes and that's why the more perpendicular the vectors themselves are,
‫the bigger their product and the more parallel they are, the smaller their product.
‫If V one and the two are completely parallel, then their cross product would be zero because then V
‫two wouldn't have any perpendicular component to the vector V one and went V one.
‫And we two are completely perpendicular.
‫That you have 90 degrees here.
‫Well, then their cross product will be the biggest in terms of magnitude.
‫Now, the direction of the one across the EU is determined by the right hand rule, if you want to know
‫the direction of the one crossfield to the new first point, your right hand fingers in the direction
‫of the EU, one like this, and then you turn them in the direction of the two and your thump on your
‫right hand will give you the direction of the one cross the two.
‫However, if you want to find V to cross V one, then it is in reverse like this, your right hand fingers
‫first point in the direction of V to then you turn your fingers in the direction of the one and your
‫thumb will point down, giving you the direction of V to cross V one.