Question

Let u, v and w be vectors in 3d space. prove: if u and v are both orthogonal to w, then the vector u + v is also orthogonal to w.

Answer 1

\[u\cdot w=0\]
\[v\cdot w=0\]

\[(u+v)\cdot w=u\cdot w+v\cdot w=0+0=0\]