I was looking for an intuitive definition for dot product and cross product. I have found two similar quesitions in SO, but I am not satisfied with the answers. Finally I found a possible answer here. It says dot product actually gives us a way to depict mathematically how parallel two lines are and on the other side cross products tells us how two lines are perpendicular to each other. So my question is why do we want both. Why cant we just have dot product?
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The degeneracy for an $p$-dimensional quantum harmonic oscillator is given by [ 1 ] as $$g(n,p) = \frac{(n+p-1)!}{n!(p-1)!}$$ The $g$ is the...
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