WEBVTT
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Welcome back to another cross product problem, or where
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we're trying to find the dot product of across B
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and c. Cross D. And figuring out what
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this is equal to ideally as a determinant. And
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the way that we can approach this is by taking
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see crusty and by writing it as a new vector
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. Yeah, so we're really looking at a cross
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B dot e and our cross product identities tells us
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that this is the same thing as a dot.
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Be cross E. If we expand this out,
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this is just a dot, be cross. And
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I remember E was just see cross D at this
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point, we can use the helpful identity that we've
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used in the past that says that a triple cross
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product is really The 1st, 3rd time, 2nd
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minus first at second time. Third, let's put
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that into use. This is a diet. And
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then, like I said, first times first dot
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third, that will be he got the time,
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see minus 1st and 2nd, that will be e
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dot c. Time's D. Now you'll notice that
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be dot de is just a number as his be
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dot C. Therefore, this is really a dot
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, a number of times see-1. Our Number
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of Times D. What we're really looking at is
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a dot c, times this number be dot de
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minus the number. Be dot c times a dot
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be. You will notice that this looks kind of
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like a determinant, meaning we could write this as
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the determinant of the matrix A dot c. Pierotti
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. No. And you don't see a dot de
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. So that we're looking at a dot c b
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dot de minus b dot c a dot de.
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And that is what this dot product of cross products
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is equal to control.