if you draw 2 vectors from the same point, the dot product is the vector that leads from the end of the first vector, to the end of the second vector. In game dev, vectors are normally normalized, on 2 normal vectors, the dot product can be thought of as “the difference of angles between the 2 vectors”. This is useful for things like knowing if the player is pointing at something or not since you can take the looking vector, and the vector to thing, normalize both and dot them together and you know how close the player is to looking at thing.
a vector cross product gives you a vector that is perpendicular to both input vectors that is the “area” between the vectors long. (in practice, this length is just normalized away) this is useful for things like “The player is pointing this way, and the ground is this way, so which direction is right next to the player?”
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