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## Homework Statement

Find some* vector funcion r with domain (-∞,∞) whose image is the intersection of the two surfaces:

x²+y²+z²=9,

x+y+z=3.

*: vector fuction must not contain inverse trig functions or +/ square routes.

**2. Gameplan**

Well, what I started to do was draw a picture of the plane cutting through the sphere, luckily the radius of it was 3 and the x,y,z intercepts of the plane landed on the sphere too. So I thought I could set the equations equal to eachother and from there find a parametric function that I can put into a vector function form.

## The Attempt at a Solution

What I had found for setting both equations equal to eachother is

x²+y²+z²=3x+3y+3z

=

(x-3/2)²+(y-3/2)²+(z-3/2)²=27/4

from this, this gives me an equation on a sphere which confuses me becuase I thought that the intersection of two surfaces would be a line (which I hoped to have happen when setting both equations equal to eachother)

Also, I've found the centroid of triangle formed by the x,y,z intercepts of the plane which is (1,1,1). The closest point from the centroid to the surface of the sphere is (sqrt(3),sqrt(3),sqrt(3)).

Much help would be appreciated

Thanks