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in this video weamp;#39;ll present two proofs for the fact that this formula actually represents the dot product of vectors V and W in terms of their components with respect to a Cartesian basis that is this expression equals the length of V times the length of W times the cosine of the angle between them the first proof will rely on a little bit of trigonometry but just a little bit and the second proof will rely seemingly on nothing at all and will actually give rise to a lot of new ideas so letamp;#39;s start with the first maybe more boring proof that relies on trigonometry but it only relies on this one trigonometric identity and if you donamp;#39;t remember the identity for the cosine of the sum of two angles in a few videos when we talk about rotations in the plane and their matrix representations youamp;#39;ll have a great mnemonic rule for remembering this formula if you ever forget it so given this formula we can derive the formula for the cosine of the difference we just
