MATH 32A Midterm: Math 32A Exam 4
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Practice for midterm i (solutions: let p , q and r be three points and a = Show that a b + a c + b c = 2 (hint: how long is a + b + c?) We have a + b + c = Rp = 0, the all 0-vector since we will start and stop at the same point. In particular, in answer to the hint, we have that a + b + c has length 0. But we can nd the length (or more precisely length squared) by using the dot product (and there are dot products in the above equation). 0 = (a + b + c) (a + b + c) = a a + a b + a c + b a + b b + b c + c a + c b + c c.
