Is there a general theorem for lines intersecting in $R^2_{++}$ space?

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Im wondering if there is a general theorem which discusses whether or not two lines that intersect in the $\mathbb{R}_{++}^2$. This is visualized in the graph below. enter image description here

If there is a broader theorem discussing if multiple lines intersecting in this space or in higher dimensions in terms of planes that would be useful as well.

Does such a theorem exist?