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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.
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Now, you can think about what this is.
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This is every mass multiplied by its position.
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So, take this guy, sum over i, mi·ri,
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divide it by the total mass, and multiply it by the total mass.
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But what is this?