Iloczyn wektorowy (Cross product). matfilmy; 7 videos Mnożenie wektorowe – reguła prawej dłoni (geometria analityczna). by eTrapez. iloczyn wektorowy translation in Polish-English dictionary.
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It’s a1 times a2 b3 minus a1 times that. In the formula known today as the Biot —Savart – Laplace law vector product appears. And then I’m going to subtract an axbxcx, minus axbxcx. It’s a little bit messier, but let me just– so I could write this i there and that i there.
And then you do the same thing for the c, cx, cy, cz.
Look carefully at theFigure 1, analyze the vectors position, practice on your own hand. Notice that I didn’t say that any of these guys up here had to be nonzero. Remember, when you take the dot product of two things, you get a iloczgn quantity.
So b2 a3 b1 minus b2 a1 b3. And I’m going to cross that with the vector b and it has three components: But when I first introduced it, I mentioned that this was only one type of vector multiplication, and the other type wektoroyw the cross product, which you’re probably familiar with from your vector calculus course or from your physics course. With this formula we get: I’m going to factor the bx out.
So let me just multiply it out. That forms a plane. Diagram illustrating the dot and cross products together. Let me draw it all. Applications Vector product has a lot of useful interpretation both physical and geometric.
Now what does this become?
This is ioczyn really one expression, I’m just writing it on multiple lines. Vector product of vectors and is defined as. And then we’re going to want to subtract. It can be accepted left handed rule, then we go clockwise and use the left hand rule. Actually, let me write it a little bit differently.
So what I’m going to do is I’m going to get rid of the minus and the j, but I am going to rewrite this with the signs swapped. Probably scroll down a little bit.
That was hopefully pretty straightforward. So the next thing you’re saying well, OK.
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And then finally, plus– I’ll just continue it down here. And I could do the same things for b and c. So plus b2 times this thing. Modifications made by CheCheDaWaff. And then we also want to get rid of that right over there. This is a retouched picturewhich means that it has been digitally altered from its original version.
It can also be interpreted as: But sektorowy is this good for? That’s 2 plus We’re going to subtract a dot b times the exact same thing.
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And now what I’m going to do– this is a little bit of a trick for this proof right here, just so that we get the results that I want. And we’ll put b’s x term, b’s y coefficient, and b’s z component. And I could put the j right over there. And so a cross b will pop out like this. What is in our context, the definition of orthogonal? I know it took us a long time to get here, but iooczyn is a simplification.
Let’s see, what else do we have?
iloczyn wektorowy – Polish
And then, for the bottom row, we cross that out again or ignore it. And then we take out that column and that row, so it’s going to be bxcz– this is a little monotonous, but hopefully, it’ll have an interesting result– bxcz minus bzcx. I have the vector 1, minus 7, and 1. My motivation for actually doing this video is I saw some problems for the Indian Institute of Technology entrance exam that seems to expect that you know Lagrange’s formula, or the triple product expansion.
And the way I think about it is you take your right hand and let me see if I can draw a suitable right hand. Vector product In the space additionally to the scalar product of two vectors, which is a scalar size, there is another kind of vector multiplication. And in all of these situations, I’m just going to assume– let’s say I have vector a. They’re computationally intensive and, at least in my mind, they’re confusing.
And I’m looking at this two-by-two over here, minus bzcy. When you do it over here, you’re going to get vector c.