What is the cross product of #[-1, 2, 3]# and #[-8, 5, 1] #?

1 Answer
Nov 3, 2016

Answer:

The cross product is #=〈-13,-23,11〉#

Explanation:

If we have 2 vectors #vecu=〈u_1,u_2,u_3〉#
and #vecv=〈v_1,v_2,v_3〉#
The cross product is given by 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=〈-1,2,3〉# and #vecv=〈-8,5,1〉#
so the cross product is #〈(2-15),-(-1+24),(-5+16)〉#
#=〈-13,-23,11〉#