Can someone please explain why the cross product of AxB= the area of the parallelogram?
>>7775830
Because it's not a parallelogram.
why wouldn't it be?
>>7775830
>Can someone please explain
Yes, someone can.
>>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.
>>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.
>>7775830
Because of Fronequinns Lemma, read it up on wikipedia, idiot.
>>7775854
>Fronequinns Lemma,
>>7775830
Parallelipiped you fool
>>7775858
That's wrong you fool
Just put a set of coordinates, parameterize everything, compute the area and see for yourself, geez. That's what coordinates are for.
It is actually defined that way (+right hand rule and perpedical to both a and b).
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
https://youtu.be/KDHuWxy53uM
https://youtu.be/pJzmiywagfY
Maybe this can help?
>>7776158
k i gotta admit, im impressed google
>>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.
I hope this helps. http://eli.lansey.net/btg02-dtcrprd.pdf
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/
>>7775837
can i go to the bathroom?
>>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
>>7777911
youre fucking autistic
>>7777901
Underrated post
