Help on REALLY SIMPLE physics

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.

 Spoiler

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.

See, here's where my brain burns, I had the thing done already but I made a tiny mistake...

first time for some reason I got that r1 x r2 was -10i +7j + 7k and |r1xr2| was sqrt(198) then I realized that that -10 was wrong but didn't go back to the |r1xr2| so didn't correct it... stupid mistakes I make because I've lost habit. Thanks for making me see it.