To check whether two 2D lines are coincident, the distance of and to need to be calculated. For a coincident line both need to be (almost) zero.
The z component of the cross vector can be used for this quite elegantly.
Note: The cross vector is noted as an x e.g. x
To check whether the two lines and are coincident, the z-component of two cross vectors need to be calculated. Both calculate the distance of the points on line to .
x is the area of the parallelogram , dividing it with the length of () gives the shortest distance of point to line .
x gives the area of the parallelogram
After dividing with this is also the shortest distance of to line . If both distances are small enough the lines are coincident.