2011-12-12, 05:07 PM
http://en.wikipedia.org/wiki/Cross_product
How it actually equates to the area of a parallelogram requires some more insight than what your current level seems to suggest, I believe.
r1 x r2 = det(i j k; 2 3 -1; -1 2 -3) = (3*(-3) - 2*(-1))*i + ((-1)*(-1) - (-3)*2)*j + (2*2 - (-1)*3)*k = -7i + 7j + 7k
length(r1 x r2) = length(-7i + 7j + 7k) = sqrt(3 * 7^2) = sqrt(147)
Alternatively:
||r1 x r2|| = ||r1||*||r2||*sin(r1, r2), if you have the angle, which you don't.
Well, technically you can find the dot product and then divide by the lengths to get the angle, but that's just roundabout work.
If you tried it this way and didn't get it to work, I'm fairly confident you just made a computation mistake.
Cross product really is just voodoo magic if you haven't taken Linear Algebra. There are ways to memorize how to take it, or you can just plug and chug with this formula.
How it actually equates to the area of a parallelogram requires some more insight than what your current level seems to suggest, I believe.
r1 x r2 = det(i j k; 2 3 -1; -1 2 -3) = (3*(-3) - 2*(-1))*i + ((-1)*(-1) - (-3)*2)*j + (2*2 - (-1)*3)*k = -7i + 7j + 7k
length(r1 x r2) = length(-7i + 7j + 7k) = sqrt(3 * 7^2) = sqrt(147)
Alternatively:
||r1 x r2|| = ||r1||*||r2||*sin(r1, r2), if you have the angle, which you don't.
Well, technically you can find the dot product and then divide by the lengths to get the angle, but that's just roundabout work.
If you tried it this way and didn't get it to work, I'm fairly confident you just made a computation mistake.
Cross product really is just voodoo magic if you haven't taken Linear Algebra. There are ways to memorize how to take it, or you can just plug and chug with this formula.
Spoiler
![[Image: 8f95c2f2e99b34e0698be10d2c24416c.png]](http://upload.wikimedia.org/wikipedia/en/math/8/f/9/8f95c2f2e99b34e0698be10d2c24416c.png)