Scalars and Vectors in Physics

A scalar is fully described by a number and a unit, while a vector also carries a direction, and that extra piece of information is why the rules here do not look like ordinary arithmetic. Adding two vectors is not the same as adding two numbers, because where they point decides the answer. The blocks work through the arrangement of the vectors first, then the algebra that ignores direction altogether, and finally the component method that turns vector addition back into ordinary arithmetic.