Show that the vector $(\vec{a}+\vec{b}+\vec{c})$ is perpendicular to the plane

Question

Problem: Show that the vector $(\vec{a}+\vec{b}+\vec{c})$ is perpendicular to the plane through the extremities of the vectors $\vec{b}\times \vec{c}, \vec{c}\times \vec{a}$ and $\vec{a}\times \vec{b}$.

Answer 1

HINT: To show that $\vec v$ is orthogonal to the plane through $\vec A$, $\vec B$, and $\vec C$, you must show it is orthogonal to each of the vectors $\vec B-\vec A$ and $\vec C - \vec A$. (Why?)