How do you calculate the cross product of two vectors?
To calculate the cross product of two vectors you take the coordinates of vector 1 which are (x1,y1,z1) and the coordinates of vector 2 which are (x2,y2,z2) and put these coordinates into a 3x3 matrix. On the first row of the matrix you have i, j, k; on the second row of the matrix you have x1, y1, z1; and on the bottom row x2, y2, z2. You then calculate the determinant of this matrix.
To do this you multiply i by (y1*z2 - z1*y2) then subtract j multiplied by (x1*z3 - x3*z1) and add k multiplied by (x1*y2 - x2*y1), the resultant vector is the cross product of the original vectors.
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Answered by Michael K. • Further Mathematics tutor
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