Cartesian Notation of a Vector
Unit Vectors and Vectors
Using a unit vector, that is a vector whose length is 1, we can write any vector as , where is the length of and is the unit vector that defines the direction of .
Cartesian Notation of a Vector
We can extend in a natural way the description of the position of any point using Cartesian coordinates to vectors.
By associating with the x-axis its unit vector and with the y-axis its unit vector , we can write any vector as the combination of its oriented components using the Cartesian notation:
.
Test Yourself...
Write the following vectors in Cartesian notation: - The tail of is at the origin, and the tip is at the point . - The tail of is at and the tip is at . - is the opposite of .