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

Nov 3, 2016

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))∣

$= \vec{i} \left({u}_{2} {v}_{3} - {u}_{3} {v}_{2}\right) - \vec{j} \left({u}_{1} {v}_{3} - {u}_{3} {v}_{1}\right) + \vec{k} \left({u}_{1} {v}_{2} - {u}_{2} {v}_{1}\right)$

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〉