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Can someone please explain why the cross...
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Can someone please explain why the cross product of AxB= the area of the parallelogram?
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>>7775830
Because it's not a parallelogram.
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why wouldn't it be?
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>>7775830
>Can someone please explain
Yes, someone can.
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>>7775836
Because it's clearly a representation of axis, like xyz. The XY area is usually drawn as a parallelogram, so we can understand that it is a 3-dimensional image. It is actually a rectangle, or a square.
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>>7775830
because we define the sine between two angles from the cross product (the cosine comes from the scalar product).

It also happens that a.b.sin(theta) is also the surface of a parallelogram with sides a,b and an angle theta between them.
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>>7775830
Because of Fronequinns Lemma, read it up on wikipedia, idiot.
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>>7775854
>Fronequinns Lemma,
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>>7775830
Parallelipiped you fool
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>>7775858
That's wrong you fool
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Just put a set of coordinates, parameterize everything, compute the area and see for yourself, geez. That's what coordinates are for.
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It is actually defined that way (+right hand rule and perpedical to both a and b).
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It's a special case of the relation between determinants and volume. And that relation is proved from standard properties of determinants... Effect of shearing transforms, etc
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https://youtu.be/KDHuWxy53uM
https://youtu.be/pJzmiywagfY

Maybe this can help?
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>>7776158
k i gotta admit, im impressed google
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>>7775830
Because it is the determinant of a matrix, in terms of the operation to find it.

You'll learn why in an introductory linear algebra course. If you don't your uni is shit.
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I hope this helps. http://eli.lansey.net/btg02-dtcrprd.pdf
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the cross product of $\mathbf{A}$ and $\mathbf{B}$ can be expressed as $\Vert \mathbf{A} \Vert \Vert \mathbf{B} \Vert \sin(\theta)~ \mathbf{n}$ where $\mathbf{n}$ is the normal vector of the plane spanned by $\mathbf{A}$ and $\mathbf{B}$

next time, try drawing a picture instead of making a thread
or at least post it in the /sqt/
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>>7775837
can i go to the bathroom?
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>>7777897
OP's question was pretty retarded and lazy to begin with

but your answering a question with circular logic

hes asking for a derivation of the formula not plug and chug you retard
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>>7777907
that is incorrect

>>7775830
>Can someone please explain why the cross product of AxB= the area of the parallelogram?

i have answered this question sufficiently
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>>7777911
youre fucking autistic
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>>7777901
Underrated post