# List of all the cross and dot products in physics?

• Epix Trix
In summary, the calculation of many quantities involve cross and dot products, which have a geometric description as the projection and perpendicular projection of one vector onto another. Some commonly used formulae that involve cross and dot products include Lorentz force, angular momenta, torque, work done, direction of magnetism, fluid flow, Poynting vector, and energy density in electromagnetic theory. The del operator, which includes the gradient, divergence, and curl, can also be included in the search for more examples.

#### Epix Trix

the calculation of many quantities involve cross and dot products in their formulae.

For cross products, i only know of three: lorentz force, angular momenta and torque.
For dot products, i only know of one: work done

im hoping to add more to my list. Can you guys help me include other commonly used formulae which also involve cross and dot products?

dot products have a geometric description as the projection of one vector on another

and similarly for cross product where you get the perpendicular projection of one vector on another.

EM theory uses vector cross product for direction of magnetism relative to current flowing through a wire and vice versa.

(force dot dr) as a differential for work (ie integrate over it to get the work done)

p v dot dS for fluid flow out of a surface differential where p is the fluid density and v is the velocity

EM theory f = q (E + v x B)

EM theory the poynting vector P = E x H

and energy density of the EM field W = 1/2 (E dot D + H dot B )

Relativity may have other examples as well.

i don't think there are any unique examples of cross and dot products in SR

but thanks for the lengthy reply

you could extend your search to include the del operator ie the gradient, the divergence and the curl.