# Cross product in four dimensions?

• Dec 4th 2011, 11:25 PM
tubetess123
Cross product in four dimensions?
Hello,

I need to take the cross product of two four dimensional vectors, but I can't find help anywhere except for up to 3 dimensions.

Thanks!
• Dec 4th 2011, 11:32 PM
redsoxfan325
Re: Cross product in four dimensions?
Quote:

Originally Posted by tubetess123
Hello,

I need to take the cross product of two four dimensional vectors $\displaystyle v_1$ and $\displaystyle v_2$, but I can't find help anywhere except for up to 3 dimensions.

Thanks!

The cross product is only defined in three dimensions. However, you can always find a vector $\displaystyle w$ orthogonal to $\displaystyle v_1$ and $\displaystyle v_2$ (I named your vectors) by solving the two equations $\displaystyle \langle v_1,w\rangle=0$ and $\displaystyle \langle v_2,w\rangle=0$.
• Dec 5th 2011, 12:00 PM
tubetess123
Re: Cross product in four dimensions?
So what about finding the points on two lines that are of minimum distance from each other?