Magnitude and Direction of Vectors
Magnitude of a Vector
The magnitude of a vectoris the distance between the initial pointand the end point. In symbols the magnitude ofis written as.
If the coordinates of the initial point and the end point of a vector is given, theDistance Formulacan be used to find its magnitude.
Example 1:
Find the magnitude of the vector的初始化ial pointis atand end point is atis at.
Solution:
Use the Distance Formula.
Substitute the values of,,, and.
The magnitude ofis about.
Direction of a Vector
The direction of a vector is the measure of the angle it makes with ahorizontal line.
One of the following formulas can be used to find the direction of a vector:
, whereis the horizontal change andis the vertical change
or
, whereis the initial point andis the terminal point.
Example 2:
Find the direction of the vector的初始化ial pointis atand end point is atis 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 vectorhas a direction of about.