CoCalc -- 2015-02-06-190915-3d.sagews

	Plot vector field $\vec{F}(x,y,z)$
	$\vec{i} +$ $\vec{j} +$ $\vec{k}$
	Box: $\leq x \leq$ $,\quad$ $\leq y \leq$ $,\quad$ $\leq z \leq$
	Plot parametric curve $C$ given by $\vec{r}(t)$ for $\leq t \leq$
	$\vec{i} +$ $\vec{j} +$ $\vec{k}$
	Plot parametric surface $S$ given by $\vec{r}(u, v)$ for $\leq u \leq$ $,\quad$ $\leq v \leq$
	$\vec{i} +$ $\vec{j} +$ $\vec{k}$

Axes

Origin

Unit normals to

S

Try to compute flux/circulation

Interact: please open in CoCalc

Notes

If you have vanishing denominators and things don't work, try to change $xyz$ -limits a little, e.g. $\vec{F} = (1/x, 0, 0)$ does not work for $x$ limits $[-1,1]$ , but $[-1.1, 1]$ is OK.
To work with 2D curves and fields (and to compute the flux across $C$ ), set $z$ -components to zero.