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all right on to probably one of the more difficult things to show the alternate form the dot product thereamp;#39;s an easy way to do this going back to a work equals Force Times distance but thatamp;#39;s not how this textbook is going and either way youamp;#39;d have to do this picture proof whether you start off with the alternate form and go back to the u1 v1 plus u2 v2 form or you go the other direction well weamp;#39;re going to just going to go the other direction so to solve this alternate form weamp;#39;re going to take vector U and vector V and draw it in this picture you know hereamp;#39;s vector u hereamp;#39;s vector V the only thing that canamp;#39;t happen is you would cannot be a scalar multiple of V so they have to be pointing in slightly different directions alright so if weamp;#39;re going to do this set up we have this nice little triangle itamp;#39;s not a right triangle we have an angle down here that Iamp;#39;m interested in because I really would love
