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.

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Clockwise and anticlockwise don't mean anything in three dimensions. – Robin Chapman Dec 6 2010 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 2010 at 11:18