1. Vectors: 5 Minute Review
Vectors can be added or subtracted.
To add vectors graphically, draw one after the other, tip to tail.
To add vectors algebraically,
Resolve the vectors into components.
Add the components of each direction.
Use the Pythagorean Theorem to find the magnitude of the resultant vector and inverse tan to find the angle.

2. Vector Addition Example
A boy pushes horizontally on a wagon with a force of 10 N. A girl pulls on the wagon’s handle at an angle of 30 degrees from the horizontal with a force of 8 N. What is the net force acting on the wagon?
Solve this problem, then ask wouldn’t it be easier to leave everything in terms of components?

3. Unit Vectors
A unit vector is a vector that points along the x, y or z axis and is one unit long.
The symbols for the x, y, and z unit vectors are
Any vector can be expressed as a sum of its x, y and z components multiplied by unit vectors.
The dimensions of the quantity are stated along with the unit vectors, e.g.

4. ©2008 by W.H. Freeman and Company

5. Unit Vector Example
A car has a velocity of 6 m/s in a direction 30o north of east. Express this vector in terms of unit vectors. Let east be the positive x direction and north the positive y direction.

6. Operations with Vectors: Magnitude
To find the magnitude of a vector, use the Pythagorean Theorem.

7. Operations with Vectors: Addition and subtraction
To add two vectors, add their components.