What is the cross product of #[9,4,-1]# and #[2, 5, 4] #?

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Answer 1 · 2015-12-13T06:28:32

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 #2,3 - 3,2#, and is 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:

#vecu = << 9, 4, -1 >>#
#vecv = << 2, 5, 4 >>#

#vecuxxvecv#

#= << (4xx4) - (-1xx5), (-1xx2) - (9xx4), (9xx5) - (4xx2) >>#

#= << 16 - (-5), -2 - 36, 45 - 8 >>#

#= color(blue)(<< 21, -38, 37 >>)#