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.