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Cross product is defined in three dimensions the resulting vector have the same magnitude as the area of the parallelogram formed by the 2 multiplied vectors and its direction direction is perpendicular to the first two vectors. so Can we come up with an equation using the same analogy but in 4-dimensional space(so that the resulting vector's magnitude is the volume of the parallelepiped formed by the three input vectors and it's direction is -somehow- perpendicular to the first three vectors)?

Khaled Oqab
  • 101
  • as you will see in some of the answers at the earlier version of this question, you can put your three vectors as three rows of a 4 by 4 matrix. Then make up new variables, maybe $W,X,Y,Z,$ and put those variables as the fourth row. Find the determinant of the 4 by 4 matrix, which is a polynomial $c_W W + c_X X + c_Y Y + c_Z Z.$ Your desired vector is $(c_W, c_X, c_Y, c_Z)$ – Will Jagy Jan 30 '19 at 19:57
  • parisize = 4000000, primelimit = 500000 ? h = [ 1,2,3,5; 7,11,13,17; 19,23,29,31; w,x,y,z] %1 = [ 1 2 3 5]

    [ 7 11 13 17]

    [19 23 29 31]

    [ w x y z]

    ? poly = matdet(h) %2 = 8x + (-70w + (78y - 36z)) ? col %3 = col ? col = [ -70; 8; 78; -36] %4 = [-70]

    [ 8]

    [ 78]

    [-36]

    ? h * col %5 = [ 0]

    [ 0]

    [ 0]

    [8x + (-70w + (78y - 36z))]

    ?

     – Will Jagy Jan 30 '19 at 20:02

0 Answers0