Why the outward unit normal to the plane $z=0$ is $-\vec{k}$
this question arised because i am solving to find total flux from the unit cube $0\le x,y,z\le 1$
So in the book the unit normal vector of $z=0$ ,$x=0$ and $y=0$ are taken as:$-\vec{k},-\vec{i},-\vec{j}$ respectively.
can i get some clarity how outward unit normal direction is decided?
Best Answer
The cube is in the first octant. The plane $z=0$ represents the $XY$ plane, for which there are two possible normal unit vectors: $\hat k$ and $-\hat k$. In your case, $\hat k$ would be pointing towards the interior of the cube, so the outward unit normal vector is $-\hat k$.