We will recall how geometric objects in a plane can be described using equations. These concepts are very useful because, as everyone knows, the output periphery of an overwhelming number of electronic devices are two-dimensional (monitors, paper, projectors, etc.).
Consider an orthogonal coordinate system with axes
Another important geometric object is the vector. We will denote vectors
by lower case letters with arrows, e.g.
For obvious reasons we sometimes say that vector addition and scalar multiplication (multiplication of a vector by a number) defined in (5.1) are done „componentwise“. Equality of vectors
is defined intuitively. We say that two vectors
We can multiply a vector by a number. Can we also multiply two vectors? For that purpose
we define scalar product 48.
Standard49 scalar product of two vectors
The product is called scalar, because the result is not a vector but
a number (a scalar). Furthemore, scalar product is related to the angle between vectors. The angle
between two vectors
Length of a vector
Note that the length can be also expressed using scalar product as
You will study these and other geometric objects in the BIE-LIN course, for more than two dimensions as well.