# 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 **cyclic** and **antisymmetric**.

- 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 >>)#