Parametric equations of line in 3D space

[player1_1_1]

Hello, sorry for my Englich:D

Homework Statement

I must count a line integral on the length which lies on the line which is defined by equations:
$$\begin{cases}x^2+y^2+z^2=R^2\\ \left(x-\frac{R}{2}\right)^2+y^2=\left(\frac{R}{2}\right)^2\end{cases}$$
it is a column which is cutting a sphere

The Attempt at a Solution

I tried to assumption that $$x=t$$ and then depending on this find other functions $$y(t),z(t)$$, but the equations are not easy. I think I can find something with trigonometric functions sinus cosinus, but I am not sure; my question is then how I can easy and quickly find parametric equations of line which is make by two planes (in this case sphere and column) cutting each another? thanks for help!

 

[tiny-tim]

Hello player1_1_1!

(have a theta: θ and try using the X² tag just above the Reply box )

It's much better to have a single-valued parameter, which x isn't.

So try using the angle (from the axis of the cylinder) as the parameter.

(btw, we say "sine" and "cosine", and we usually say "curve" for a line that isn't straight … even though we say "line integral" for any curve! )