Trying to wrap my head around some mathematical concepts for game dev, thank you 🙂
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The dot product multiplies the components of both vectors that are in the same direction. For example, if you have work equals force dot displacement, it’s the portion of the force that’s along the direction of the displacement. If there’s any force that’s perpendicular to the movement, it does no work, and the dot product ignores that component.
The cross product multiplies the components of both vectors that are perpendicular to each other. For example, angular momentum is momentum going around in a circle. You can determine it as position x momentum. This isolates the component of the momentum vector that’s “orbiting” around the origin, and ignores the component that’s going toward or away from the origin. The result is a vector perpendicular to both vectors you started with, which is a little weird, but the product can have two possible directions depending on which way the object is going around, so it’s relevant that it’s a vector.
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