Addition and Subtraction of Vectors
To add and subtract vectors graphically and by components.
Vector Addition from the PhET at the University of Colorado
- To learn how to resolve vectors into components.
- To learn how to add and subtract vectors by components.
- To learn how to use vectors to calculate physics problems.
If we know the magnitude of the vector and the angle it makes with the positive x-axis , its components are equal to:
Ax = A cos(θ) and Ay = A sin(θ)
Conversely, if we know the components of a vector, then we can determine its magnitude and direction with respective to the positive x-axis.
If a vector , then its components can be calculated as:
Cx = Ax ± Bx and Cy = Ay ± By
- Open the simulation Vector Addition.
- Select “Show Grid” from the menu on the right.
Activity 1. Switch from component- to magnitude-angle representation of a vector
Calculate the magnitude and the angle with respect to the positive x-axis for the following vectors. Check with the simulation to confirm your result.
Question: For the second vector, did you get the same angle as the simulation showed?
Activity 2. Adding and Subtracting Vectors
For the vectors , , and , calculate the components, the magnitude, and the direction of each vector given in the table.
|A + B|
|B - C|
Question: Were your results confirmed by the simulation?
Activity 3. Solving a Problem
Oasis B is located 25 km east from oasis A. A camel starts from oasis A and travels 19.6 km in the direction 14.7 degrees south of east. Then it walks 8 km directly to the north. How far is the camel from oasis B?
Hint: Use the simulation to construct the path of the camel so that you can visualize the problem better.
Question: In which quadrant is the camel located after the second leg of the trip?
Submit your results to receive credit for the lab.