# determing if two line segments intersect using cross products

The following text is an extract from a pdf found online, basically the technique doesn't seem to find the point of intersection, but it says to determine if the two line segments intersect using cross products. Given the limited amount of description here, How does this technique work for determining if the two lines intersect?

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• @mathmaniage The cross product has a sign which depends on the relative orientation of two lines which meet at a point. Really that represents the choice of one of the two normals to the plane containing the lines. Here the lines are defined by three points - two on the segment and one at the end of the other segment. The two vectors for the cross product in the first case are $PQ$ and $QR$. The sign of the cross product determines whether the path $PQR$ has a left turn or a right turn. – Mark Bennet Jun 12 at 16:14