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I was wondering, why is the vector projection useful in the way that it is presented? Why isn't just the vector times cosθ sufficient to find the projection of a vector onto another one, why the dot product divided by the magnitude of the vector squared times that same vector?

The book didn't give too much insight to its usefulness other than saying ''it's important'', so it left me a little bit cliffhanging, so just looking for some clarification.

Thanks