Show that the curve,

$\displaystyle \overline{r(t)} = 4cost\overline{i} + 4sint\overline{j} - sint\overline{k}$

is in a plane, and find the equation for the plane..

If I substitute into the equation of a plane I get,

$\displaystyle a(4cost)+b(4sint)+c(-sint)+d=0$,

I see that it will hold if for example $\displaystyle b=1$ and $\displaystyle c=4$, and so I guess that I have showed that the curve is in a plane, and could use $\displaystyle [0,1,4]$ as my normal vector.

Is there a nice way of doing this so?

Thanks.