1. Vector Components

2. Coordinates Vectors can be described in terms of coordinates.
6.0 km east and 3.4 km south
1 N forward, 2 N left, 2 N up
Coordinates are associated with axes in a graph. y x
x = 6.0 m
y = -3.4 m

3. Use of Angles
Find the components of vector of magnitude 2.0 N at 60° up from the x-axis.
Use trigonometry to convert vectors into components.
x = r cos 
y = r sin 
This is called projection onto the axes. Fy Fx
Fy = (2.0 N) sin(60°) = 1.7 N
60°
Fx = (2.0 N) cos(60°) = 1.0 N

4. Ordered Set
The value of the vector in each coordinate can be grouped as a set.
Each element of the set corresponds to one coordinate.
2-dimensional
3-dimensional
The elements, called components, are scalars, not vectors.

5. Component Addition A vector equation is actually a set of equations.
One equation for each component
Components can be added like the vectors themselves

6. Vector Length
Vector components can be used to determine the magnitude of a vector.
The square of the length of the vector is the sum of the squares of the components.
4.6 N
2.1 N
4.1 N

7. Vector Direction
Vector components can also be used to determine the direction of a vector.
The tangent of the angle from the x-axis is the ratio of the y-component divided by the x-component.
4.6 N
2.1 N
q = 27
4.1 N

8. Components to Angles
Find the magnitude and angle of a vector with components x = -5.0 N, y = 3.3 N. y x
x = -5.0 N L
y = 3.3 N 
L = 6.0 N
 = 33o above the negative x-axis

9. Alternate Axes
Projection works on other choices for the coordinate axes.
Other axes may make more sense for a particular physics problem. y’ x’  f f
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