If a→,b→,c→ are non-coplanar vectors and r→⋅a→=r→⋅b→=r→⋅c→=0 then
r→⊥(c→×a→)
r→⊥(a→×b→)
r→⊥(b→×c→)
r→=0→
Let r→≠0→. Then r→⋅a→=r→⋅b→=r→⋅c→=0
hence a→,b→ and c→ are coplanar, which is a contradiction.
Therefore, r→=0→