Question

What is the direction of the outward normal to x2 + y2 + z2=1 at (1,1,1)

Answer 1

\[x^2+y^2+z^2-1=0\]
\[\nabla(x^2+y^2+z^2-1)=2(x\,\vec{i}+y\,\vec{j}+z\,\vec{k})=2\,\vec{r}\]
\[\vec{r}\quad-radius\enspace vector\]