Vector Sum
This activity belongs to the GeoGebra book GeoGebra Principia.
If there's a mathematical branch where traditional algebra and geometry naturally blend, it's in analytic geometry, the core of dynamic geometry programs like GeoGebra.
One of the key concepts in analytic geometry is that of a vector. Its graphical representation as an arrow prompts us to think about movement, about dynamism. We will use vectors to create dynamic procedures, which are very simple yet incredibly powerful, allowing us to address various situations.
The hands of an analog clock can serve as an illustration of vectors. The tip of the hour hand traces a circle, much like the tip of the minute hand. When we combine both vectors, we obtain a more intriguing path (this path intersects itself at 11 points, assuming the minute hand is longer than the hour hand, in 11 different directions, which means that within 12 hours, the vector sum of both hands coincides 121 times). If we also include the second hand, vector addition leads to an even more complex trajectory.
Vector sum open the door to the simulation of balances of forces. Thanks to vectors, we can simulate forces, whether attractive or repulsive, that compel a point to seek a relatively stable position (or path), one that is in equilibrium with respect to other forces or constraints.
- Note: For a better view of the construction, it is recommended to download the ggb file here.
Author of the construction of GeoGebra: Rafael Losada.