Multivariable Calculus | The Cross Product

We define the cross product, give a few examples, and state a few properties.

[thatonemailbox]

7:40 YOU DID THE WALTER LEWIN DOT LINE

[mingmiao]

Thanks Michael. Although there is no unique way to teach a notion, I find it makes more sense for students if the cross product is taught in the following way: First, give a few motivations from physics such as torque and Lorentz force. Second, define the cross product geometrically. Then, deduce the basic algebraic properties of the cross product from its geometric definition. Finally, derive the coordinate formula (that is often provided as the 1st definition of CP) using the algebraic properties.

[seanhunter]

That method of calculating the cross product (which I think is called a Laplace expansion-could be wrong) always troubles me. I know it works mechanically, but the 3x3 matrix you start with is weird- its second two rows are vectors of real numbers but its first row is a vector of basis vectors. I thought all the entries in a matrix had to come from a field - I'm struggling to understand how you can have a field where things can be either a number or a vector.

[uea]

you are the best but please don't ever use that red chalk ever again, it hurts my ears