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Cross product question

Posted by sirius

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sirius

Cross product question
August 28, 2006 12:41PM

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When calculating the cross product of two vectors (u and v) to get a new vector (w), you use the following formula:

wx = vy*wz - vz*wy
wy = vz*wx - vx*wz
wz = vx*wy - vy*wx

Now, my question relates to the calculation of wy. It seems "arse-about-face" to me. Why is it not:

wy = vx*wz - vz*wx

Does anyone understand this? Am I being stupid?

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chaospixel

Re: Cross product question
August 29, 2006 12:50PM

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look here:
http://mathworld.wolfram.com/CrossProduct.html

the first equation they give shows why it seems arse-about-face. notice that it is initially given as +x, -y, +z, then when you multiply by -1 (for the y component) you get the version you posted earlier.

I find the determinant notation the most convenient for remembering the formula (and that helps explain why the y component is negative).

http://en.wikipedia.org/wiki/Cross_product
has a lot more detail on cross products.