How do I multiply vectors?
You have two options for multiplying vectors, and your choice of which depends on your goal. If your goal is to return a scalar, you use the dot product, as indicated “D = a · b”, read aloud as “D equals a dot b”. Do not use a period to indicate dot product, it looks bad. If your goal is to return a vector, you use the cross product, as indicated “c = a × b”, read aloud as “c equals a cross b”. It is OK to use an x to indicate this multiplication, but it is better to use the official cross product symbol that I have used. Dot products return the product of the aligned components of the two factor vectors. An application of the dot product is work done by a force, as the target object moves through a distance. Cross products return a vector perpendicular to the two factor vectors (as per the right hand rule), equal in magnitude to the product of one vectors magnitude, and the magnitude of the perpendicular component of the other vector. An application of the cross product is torque, the
