Calculating a 2D Vector's Cross Product

Question

From wikipedia:

the cross product is a binary operation on two vectors in a three-dimensional Euclidean space that results in anothe

Answer 1

Another useful property of the cross product is that its magnitude is related to the sine of the angle between the two vectors:

| a x b | = |a| . |b| . sine(theta)

or

sine(theta) = | a x b | / (|a| . |b|)

So, in implementation 1 above, if a and b are known in advance to be unit vectors then the result of that function is exactly that sine() value.