Prove Tetrahedron Opposite Vectors add to $0$

Question

I really need help on this problem, I'm in Multivariable Calculus (Calc III) and I just can't solve this.

Let $v_1$, $v_2$, $v_3$, and $v_4$ be vectors whose lengths are equal to the areas of the sides of a tetrahedron and are perpendicular to those sides yet pointing outward. Show that $v_1+v_2+v_3+v_4=0$.

Answer 1

$a \times b+b\times c+a\times c + (b+c)\times (a+b)=0$, see Cross product