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 [math] \mathbf{A} [/math] and [math] \mathbf{B} [/math] can be expressed as [math] \Vert \mathbf{A} \Vert \Vert \mathbf{B} \Vert \sin(\theta)~ \mathbf{n} [/math] where [math] \mathbf{n} [/math] is the normal vector of the plane spanned by [math] \mathbf{A} [/math] and [math] \mathbf{B} [/math]

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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>>7777911

youre fucking autistic

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>>7777901

Underrated post

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