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But in this problem, there's a very nice solution.
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There's stuff I don't want that is going to vanish.
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It's going to vanish.
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And let's see why it vanishes.
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Let's take the cross terms.
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The cross terms are like the 2A dot B terms.
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So, here is the 2.
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One of the vectors A is the vector d.
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And it's going to be taking the dot product with mi·ri summed over i
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because there's going to be a d dot ri twice.
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But d is not dependent on the summation index.
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It's common to all the terms in the sum and you pull it out.