How to calculate Vector Cross Product

CaseyL

From the documentation it looks like the * operator will perform a cross product and ;* will perform a dot product. I want to use a cross product to determine the vector normal to a pair of known vectors like this:

 

p1 = [1, 2, 4];
p2 = [2, 1, 4];
p3 = [2, 2, 4];

v1 = p3 - p1;
v2 = p2 - p1;

xProd = v1*v2;

 3 points define a plane, two vectors taken from those points do the same, the cross-product should give the normal vector of that plane. The problem seems to be that the dimensions of the two matrices being multiplied (v1 and v2) do not agree -- nRows(v1) should equal nCols(v2). I can implement this manually with a simplified formula for vector cross products but does anyone know how to format this differently to work with matrix multiplication?

cwillden

If you're only ever dealing 3x1 (or 1x3) vectors, then I would think computational efficiency or elegance is not too important.  Would this be sufficient?

cross_prod = function({v1, v2},
	matrix({v1[2]*v2[3] - v1[3]*v2[2], v1[1]*v2[3] - v1[3]*v2[1], v1[1]*v2[2] - v1[2]*v2[1]});
);

cross_prod(v1, v2);