Thread: [SOLVED] Vector equation for the intersection between surfaces.

1. [SOLVED] Vector equation for the intersection between surfaces.

Find a vector equation for the intersection of the surfaces x^2+y^2=25 and z=x+y. (Hint: What is the geometric object described by x^2+y^2=25? How can you write that in parametric form?)

I realize that x^2+y^2=25 is a circle, and I'm pretty sure I have to solve for one of the variables in the second surface and substitute into the first surface, but I don't know where to go after that. Any help would be greatly appreciated!

2. Originally Posted by pedro2208
Find a vector equation for the intersection of the surfaces x^2+y^2=25 and z=x+y. (Hint: What is the geometric object described by x^2+y^2=25? How can you write that in parametric form?)

I realize that x^2+y^2=25 is a circle, and I'm pretty sure I have to solve for one of the variables in the second surface and substitute into the first surface, but I don't know where to go after that. Any help would be greatly appreciated!
By your hint note that $x^2+y^2=5^2$ is an infinite circular cylindar center on the z-axis. In poloar coordinates it has the equation $r=5$

Remember that $x=r\cos(\theta)=5\cos(\theta)$ and

$y=r\sin(\theta)=5\sin(\theta)$ and

$z=x+y=5\cos(\theta)+5\sin(\theta)$ so finally

$v(\theta)=5\cos(\theta) \vec i +5\sin(\theta) \vec j + (5\cos(\theta)+5\sin(\theta))\vec k$

3. Thank you! I completely forgot about changing it to polar coordinates. I appreciate the help!