What is the cross product of [9,4,-1] and [2, 5, 4] ?
1 Answer
Dec 13, 2015
The cross product of two 3D vectors is another 3D vector orthogonal to both.
The cross product is defined as:
color(green)(vecuxxvecv = << u_2v_3 - u_3v_2, u_3v_1 - u_1v_3, u_1v_2 - u_2v_1 >>)
It is easier to remember it if we remember that it starts with
- it cycles as
2,3 -> 3,1 -> 1,2 - it is antisymmetric in that it goes:
2,3 //3,2 -> 3,1 //1,3 -> 1,2 //2,1 , but subtracts each pair of products.
So, let:
= << (4xx4) - (-1xx5), (-1xx2) - (9xx4), (9xx5) - (4xx2) >>
= << 16 - (-5), -2 - 36, 45 - 8 >>
= color(blue)(<< 21, -38, 37 >>)
