# Detect if directed cycle is clockwise or counterclockwise in 3D [closed]

I need to check if cycle given by $(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3, y_3, z_3)$ is clockwise or counterclockwise. I have found this answer: Detecting whether directed cycle is clockwise or counterclockwise but I don't have a clue how to make it work for 3 dimensional space.

-
Clockwise and anticlockwise don't mean anything in three dimensions. –  Robin Chapman Dec 6 '10 at 10:22
To extend Robin's remark, you need a specified direction $u$ (perhaps the $z$-direction). Then you can determine if the cycle is cw or ccw with respect to $u$. –  Joseph O'Rourke Dec 6 '10 at 11:18

## closed as off topic by Denis Serre, Douglas Zare, Tim Perutz, Qiaochu Yuan, Pete L. ClarkDec 6 '10 at 18:18

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.