Vector Addition and Subtraction Simulation
Vectors add head to tail, not by simple arithmetic. This simulation lets you drag vectors around and see the resultant form graphically, with the component breakdown shown alongside so the two methods can be checked against each other.
How to use this simulation
- Drag vectors to change magnitude and direction
- Switch between graphical and component methods
- Add a third vector to the sum
What to look for
- The resultant closes the polygon from the first tail to the last head
- Perpendicular vectors give a resultant found by Pythagoras
- Reversing a vector and adding is identical to subtracting it
The physics behind it
Vectors combine head to tail, or equivalently by adding their components: the resultant has components (aₓ + bₓ, a_y + b_y). Subtraction a − b is addition of the reverse vector −b. Two vectors of given magnitudes produce a resultant anywhere between their sum, when parallel, and their difference, when antiparallel.