 Related Topics:
Common Core (Vector and Matrix Quantities)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn to add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

### Suggested Learning Targets

• I can add vectors graphically using the Parallelogram Method.
• I can add vectors using the Parallelogram Method, Law of Cosines and Law of Sines.
• I can add vectors graphically using the End-to-End method.
• I can add vectors using the End-to-End method, Law of Cosines and Law of Sines.
• I can add vectors using the Component Method.
Common Core: HSN-VM.B.4ab

The following diagrams show how to add vectors graphically using the Triangle or Head-to-Tail Method and the Parallelogram Method. Scroll down the page for more examples and solutions. ### Parallelogram Method

Adding Vectors Graphically - Parallelogram Method
This video shows you how to add vectors graphically using the parallelogram method.

Graphical Method of Vector Addition (Parallelogram Method) Vector Addition with Parallelogram Method
A problem of finding the resultant of the addition of two force vectors, using the parallelogram method (a geometric solution involving the law of cosines and law of sines).

### End-to-End Method

Adding Vectors Graphically - Tip-To-Toe Method
This video shows you how to add vectors graphically using the tip-to-toe method. How to Add Vectors Graphically (end-to-end). Vector Addition: head-to-tail method
Add two vectors graphically using the head-to-tail method. Vectors using law of sines and cosines
A problem of finding the resultant of the addition of two force vectors, using the head-to-tail method.

### Component Method

How to Add vectors using components (part 1)
An example of how to add two vectors by using their components. This video goes through breaking them down, and adding the components. How to Add vectors using components (part 2). Vector Addition with Components
A displacement problem is presented showing how to add vectors together using the component method.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  