Magnitude and Direction of Vectors
Magnitude of a Vector
The magnitude of a vector is the distance between the initial point and the end point . 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.
Find the magnitude of the vector whose initial point is at and end point is at is at .
Use the Distance Formula.
Substitute the values of , , , and .
The magnitude of is about .
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 is the horizontal change and is the vertical change
, where is the initial point and is the terminal point.
Find the direction of the vector whose initial point is at and end point is at is at .
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 .