The dot product is one of those elusive things that you aren't taught soon enough (In my opinion). If you want to do any lighting calculations yourself, then the dot product will be used extensively for diffuse calculations.
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vector
Vectors are the back bone of 3D graphics, without them, the world of computer graphics would be a very messy place. And knowing the length of them often comes in handy, especially when looking at intersections and collisions.
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