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A1 pelnts Preous Answers VonitLInAlg2 2038. The volume of the parallelepiped determined by the vectors glven by the followlng:. I(u Use thls result t0 find the valu...

Question

A1 pelnts Preous Answers VonitLInAlg2 2038. The volume of the parallelepiped determined by the vectors glven by the followlng:. I(u Use thls result t0 find the valume the parullelepiped determined by the vectors Iv = (1, $, 1), and w =1, J)

A1 pelnts Preous Answers VonitLInAlg2 2038. The volume of the parallelepiped determined by the vectors glven by the followlng:. I(u Use thls result t0 find the valume the parullelepiped determined by the vectors Iv = (1, $, 1), and w = 1, J)



Answers

Find the volume $V(S)$ of the parallelepiped $S$ in $\mathbf{R}^{3}$ determined by the vectors: (a) $u_{1}=(1,1,1), u_{2}=(1,3,-4), u_{3}=(1,2,-5)$ (b) $u_{1}=(1,2,4), u_{2}=(2,1,-3), u_{3}=(5,7,9)$

Welcome back to another cross product video. We're going to try to calculate the volume of a parallel pipe bed defined by these three vectors here. The textbook gives us a nice formula that we can use which says that it's the absolute value of a dotted with a vector secrecy. But instead of calculating across product and then adopt product, we can do this using a triple product where instead of using I J and K in our matrix. Let's get that out of here. Ed, we're going to directly plug in are vectors A. B and see So doing that. We get 1 I1J zero. Okay. zero I 1 J one K and one I one J one. Kay. Then we can calculate the cross products same as normal but anywhere we have an I. J and K. We'll use those values instead. When we ignore our first column, We're looking at one times 1 And it's one times 1. One minus one times not I but rather no. Yes. Now we ignore our second column And we look at zero times 1 -1 times one zero times one -1 times one. All multiplied by one us. We'll ignore a third column and then we'll look at zero times one -1 times one zero times one, one times 1, all multiplied by zero. Since we don't have any eyes jay's or k's, this is just a scalar and so we can add it all up. We have zero times one minus negative one and it's one plus negative one time zero at zero plus one plus zero, Giving us a volume of one unit cubed. Using the triple product method. Thanks for watching.

Fun before. So it is getting asked one. Why do you? You don't want one? 11 is equal still you know my ass wanting to minus one this deep roots to want unit you says dancer.

This video is going to cover problems 27 through 30 and we know that we want to find the volume of the parallel pipe id determined by the given vectors. Or we can do it based on the edges. So what we see is we need vectors, you B m W and then um or we could have a B and C or whatever it is, We need three factors and then we know that the formula that's going to give us the volume V will be equal to magnitude of you, uh V cross W. So what's that? We will end up getting the volume. So this could be a BNC, but we see that that's where it's all at a specific point. So it's going to be our formula for the parallel pipe ID and we'll use that for the different problems that we come across.

We have to find the border Deputy will do more. Cannot be dropped. C This includes 2123 minus 112 to 4. This is given as one into four minus two. My student minus two or minus four. Last three to minus one minus Students is given to black 16 minus nine. This is people equal to nine. Unit. You This is dancer.


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