>>12561718Its fucking obvious
Just take the square of the euclidean norm of the difference of two vectors, and expand it with the linearity rules of the inner product.
When you assemble the first vector, the second vector and their difference tip to tail, you get a triangle. Use the law of cosines to compute the square of the euclidean norm of the difference of the vectors.
There. There is your proof of the equality. Its pretty intuitively obvious that we get this result because we used a special case of the law of cosines to define the norm of a vector, and then applied linearity to that definition to define a dot product.
