Vectors¶
Vectors are objects that contain much more information than scalar magnitudes. For that reason there are many more ways to perform operations with them than with simple scalar values. While addition or subtraction of vectors are well-defined, unique operations the concept of product is much more prolific than the scalar case. In particular we will distinguish the following types of products:
Scaling involves the product of a scalar times a vector.
the so-called dot (or scalar) product involves the product of two vectors to yield a scalar.
the so-called cross (or vector) product involves the product of two vectors to yield another vector.
the so-called mixed product combines a dot and a cross product to yield an scalar.
Each of them will be described in detail over the next sections. Note that each of these operations has a geometrical interpretation that is as important to know as the basic definition of the arithmetic behind the operation. Recognizing what the operations do is key to understanding later the physics that are expressed with them.