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now i said that the dot product has many many different applications but kind of for the sake of time weamp;#39;re just going to focus on a second one by way of example i want you to think back to extension one and which of that those other results we focused on that really heavily relied on the dot product the dot products in there all the time projections right so this is going to be application two so um this bitamp;#39;s a bit tricky because um having all come from different classes i know for a fact that everyone handled projections slightly differently and thatamp;#39;s actually for a good reason thereamp;#39;s lots of different ways to compute projections or lots of different formulas much like this that are all equally valid for the projection and just like with the dot product in the first place it kind of depends like which one of these formulas will i use depends what information that i have some gets provided to me it makes it easier to use like if you knew what theta w