Magnitude and Direction of Vectors
Magnitude of a Vector
The magnitude of a vector 
is the distance between the initial point P and the end point Q . In symbols the magnitude of is written as 
.
If the coordinates of the initial point and the end point of a vector is given, the Distance Formula can be used to find its magnitude.
Example :
Find the magnitude of the vector whose initial point P is at (1, 1) and end point is at Q is at (5, 3).
Solution:
Use the Distance Formula.
Substitute the values of x1 , y1 , x2 , and y2 .
The magnitude of is about 4.5.
Direction of a Vector
The direction of a vector is the measure of the angle it makes with a horizontal line.
One of the following formulas can be used to find the direction of a vector:
, where x is the horizontal change and y is the vertical change
or
,
where ( x1 , y1 ) is the initial point and ( x2 , y2 ) is the terminal point.
Example :
Find the direction of the vector whose initial point P is at (2, 3) and end point is at Q is at (5, 8).
The coordinates of the initial point and the terminal point are given. Substitute them in the formula .
Find the inverse tan, then use a calculator.
The vector has a direction of about 59° .
