# Problems With StreamPlot

I have the following vector functions:

$$E=\left\langle \cos\left[\frac{\pi x}{5}\right]\sin\left[\frac{\pi y}{4}\right], \sin\left[\frac{\pi x}{5}\right]\cos\left[\frac{\pi y}{4}\right], \sin\left[\frac{\pi x}{5}\right] \sin\left[\frac{\pi y}{4}\right] \right\rangle$$

$$B=\left\langle -\sin\left[\frac{\pi x}{5}\right]\cos\left[\frac{\pi y}{4}\right], \cos\left[\frac{\pi x}{5}\right]\sin\left[\frac{\pi y}{4}\right],0 \right\rangle$$

And I'd like to graph each of these in a different plane, so I want to know what they look like in the $$xy$$, $$xz$$, and $$yz$$ planes. Using stream plot I got a graph of the view in the $$xy$$ plane that I was happy with but with the other perspectives I'm finding them difficult to plot and I think it's because I have to use $$x$$ and $$y$$ bounds for StreamPlot. So, I'm wondering if there is a way to graph these vector fields in the $$xz$$ and $$yz$$ plots so that I have functions that aren't varying with respect to the $$z$$ axis? Because, for example, right now what I'm doing is just replacing the $$x$$ component with the $$z$$ component and graphing but since my $$z$$ component is in terms of $$x$$ it changes with the bounds which I don't want it to do.

• does e = {Cos[\[Pi] x/5] Sin[\[Pi] y/4], Sin[\[Pi] x/5] Cos[\[Pi] y/4], Sin[\[Pi] x/5] Sin[\[Pi] y/ 4]}; SliceVectorPlot3D[e, "BackPlanes", {x, -2, 2}, {y, -2, 2}, {z, -2, 2}] give what you need?
– kglr
Feb 28, 2021 at 4:11
• YES thank you!! Feb 28, 2021 at 18:25

You might consider SliceVectorPlot3D with "BackPlanes" as the second argument:
e = {Cos[π x/5] Sin[π y / 4], Sin[π x / 5] Cos[π y/4],  Sin[π x / 5] Sin[π y / 4]};