Vectors in a plane
The disadvantage of a vector given in Cartesian coordinates is that the magnitude of the vector is not specified in the denotation.
However, you can use the Pythagorean Theorem to calculate the magnitude. If the Cartesian coordinates x and y of a vector are the sides of a right angled triangle, then the magnitude of the vector is the hypotenuse of the triangle given by:
The magnitude of a vector is written with the vectors denotation surrounded by vertical bars.
Scaling a vector
The magnitude of a vector can be extended or abbreviated when multiplied by a scalar. That is called scaling. The scalar is multiplied by each of the coordinates: