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Welcome back to another cross product problem where we're trying
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to find the volume of a parallel pipe, ed
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that have adjacent points, P Q R and S
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. Where we can calculate three vectors used for our
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triple product calculation as PQ pr and P s.
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So then PQ is just q minus p. That's
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two minus negative too. Three minus one to minus
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zero. Pr is ar minus P. That'll be
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1- negative too. Four minus one and-1
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0. And lastly ps will be three minus negative
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too six minus one. One minus zero. Now
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, the textbook gives us a nice formula for volume
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as the absolute value of a dot. With the
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vector be cross C. But instead of calculating across
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product and then a dot product, we can just
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plug in a B and C directly into our matrix
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here. So we can write for two, two
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, three, three negative one And 551 and then
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calculate the cross product. How we normally would With
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the values for two and 2 replacing I. J
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. and K. This gives us when we ignore
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the first column three times one minus negative one times
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five. And normally we multiply this by I but
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this time we don't have an eye here, we
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have four minus and we ignore our second column three
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times one minus negative one times five. That's one
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minus negative. One times five. All multiplied by
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two. Us. Same idea, ignore the third
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column three times 5-5 times three. All multiplied
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by two. Since we don't have any eyes jay's
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or K's, this isn't a vector, this is
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a scalar and so we can just add everything up
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. So we're looking at three minus negative five times
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four minus three minus negative five times two plus 15
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minus 15. Two. Putting this all together,
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we're looking at 32 minus 16 plus zero, 16
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units cubed. Using the triple product method. Thanks
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for watching