What is the cross product of [3,-1,2] and [-2,0,3] ?

1 Answer
Narad T.
Nov 5, 2016

The cross product is =〈-3,-13,-2〉

Explanation:

The cross product of two vectors vecu=〈u_1,u_2,u_3〉
and vecv=〈v_1,v_2,v_3〉 is the determinant
∣((veci,vecj,veck),(u_1,u_2,u_3),(v_1,v_2,v_3))∣

=veci(u_2v_3-u_3v_2)-vecj(u_1v_3-u_3v_1)+veck(u_1v_2-u_2v_1)

Here we have vecu=〈3,-1,2〉 and vecv=〈-2,0,3〉

So the cross product is vecw=〈veci(-3)-vecj(-13)+veck(-2〉
=〈-3,-13,-2〉
To check, we verify that the dot products are =0
vecw.vecu=(-9+13-4)=0
vecw.vecv=(6+0-6)=0

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