How to find the skew (pseudoscalar) product of vectors?
I have two questions about computational geometry at once. I need to find the skew (pseudo-scalar) product of vectors, each of which is given by two points.
I found only such information:
If the vectors are given by coordinates a(x1, y1), b (x2, y2) then the skew product [a, b] = x1y2 - x2y1.
Question 1: How is each vector defined by a single point? I understood correctly that with such an entry, it is assumed that the beginning of the vector coincides with the origin of the coordinates, and the specified coordinates of the vector are the coordinates of the end of the vector?
Question 2: If in my case each vector is given by two points, then I need to transform each of the vectors so that their origin coincides with the origin before calculating their skew product?
1 answers
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Yes, that's right.
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To perform operations with vectors, they must be applied to a single point - the origin is suitable because the area under the vectors does not change.