Beginning Math and Physics for Game Programmers

Vector Addition and Subtraction

Whether your vectors represent displacements or velocities or forces, there might be times when you need to add or subtract them. We'll revisit this process in Chapters 10, 11, 12, and 14. We'll look at this process graphically first, and then we'll throw in the numbers.

When trying to organize vector quantities graphically, it is common to use an arrow for each vector. The arrow's length corresponds to the vector's magnitude, and the way it's pointing represents the direction. Because these arrows are drawn to scale, it's important to always work within the same scale (that is, all meters or all feet, but not both). That way, a vector with a magnitude of 5m appears to be half as long as a vector with a magnitude ...