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# How can I calculate the cross product of a point with a list of vectors?

Posted 9 years ago
 I am trying to calculate field using vector summation. I have a loop (in 2D) then hopefully a helix in 3D. For each point, I need to calculate the vector r^, distances to the discretized loop. This i hope will give a list of r^'s. I then need the cross product ( J x r^) I thought I could map the function cross product for the point a=1,1,0 to the vectors, but having some difficulty. This probably will not make sense. Thank you in advance en = 2; comp = 0.2; turns = 1; (*pitch = comp*2*\[Pi]*) uStep = 0.05; (*zscale = 1/( comp*uStep);*) height = Round[turns*pitch] + 1; x[u_] := Round[en Sin[u]] + en + 1; y[u_] := Round[en Cos[u]] + en + 1; biArray = ConstantArray[ 0, {2 en + 1, 2 en + 1, 3}]; (*x and y this is for defining the helix*) biVArray = ConstantArray[{0, 0, 0}, {2 en + 1, 2 en + 1}]; (*vector 0,0,0 in x,y, and z this is for defining the vectors of the \ helix*) biRArray = ConstantArray[{0, 0, 0}, {2 en + 1, 2 en + 1}]; Do[biArray[[x[u], y[u]]] = 1, {u, 0, turns 2 Pi, 0.1}] (*For points in array which contain the helix are given \ value=1*) Do[biVArray[[x[u], y[u]]] = {x[u + 1] - x[u - 1], y[u + 1] - y[u - 1],(*z defined here as 0*)0}, {u, uStep, turns 2 Pi - uStep, uStep}](*For points in array which contain the helix direction of \ the vector*) Print[biVArray] a={1,1,0} Map[Cross[a, {biVArray}]] Attachments: