DH Algorithm - Direction of X

In Denavit-Hartenberg Algorithm, the way to assign x-axis is as follows.
Select Xk to be orthogonal to Zk and Zk-1
Considering the case where Zk and Zk-1 intersect, I can chose 2 opposite
directions of Xk which are orthogonal to Zk and Zk-1. Which is the right direction? Or is it arbitrary?
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