Multivariate Calc Question: I was wondering about why it was true that the area of a parallelogram which is ||UXV|| is also equal to ||V||sinx. So, I figured it had something to do with the law of sines. I wrote out a (sort of) proof . I'll see if I can upload it.

Question

Multivariate Calc Question:  I was wondering about why it was true that the area of a parallelogram which is ||UXV|| is also equal to ||V||sinx.  So, I figured it had something to do with the law of sines.  I wrote out a (sort of) proof .  I'll see if I can upload it.

anonymous · Answer

attachment

anonymous · Answer

Ugh, my Livescribe piece of crap took 10 years to upload a single page.

phi · Answer

Have you ever seen this derivation?

anonymous · Answer

That's basically what's in my book.  I wanted to know if it was ok to use the law of sines to show it. . .

phi · Answer

Not really, since one you have |a cross b|= |a| |b| sin theta, all you need is the definition of the sine to show the area of the parallelogram =  |a| |b| sin theta
But I admire your curiosity.