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

1 Answer
Nov 5, 2016

Answer:

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#