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## Homework Statement

Show that the circle that is the intersection of the plane x + y + z = 0 and the

sphere x

^{2}+ y

^{2}+ z

^{2}= 1 can be expressed as:

x(t) = [cos(t)-sqrt(3)sin(t)]/sqrt(6)

y(t) = [cos(t)+sqrt(3)sin(t)]/sqrt(6)

z(t) = -[2cos(t)]/sqrt(6)

## Homework Equations

## The Attempt at a Solution

At first, I tried to let z=-x-y then sub it into the equation of the sphere:

x

^{2}+y

^{2}+(-x-y)

^{2}=1

x

^{2}+y

^{2}+x

^{2}+2xy+y

^{2}=1

2x

^{2}+2xy+2y

^{2}= 1

And i stuck at here, I can't make it into a circle equation.

So, I changed another way.

I equated two equations, so it becomes:

x

^{2}+ y

^{2}+ z

^{2}-1 = x+y+z

x

^{2}+ x + y

^{2}+ y + z

^{2}+Z -1 =0

(x-1/2)

^{2}+ (y-1/2)

^{2}+ (z-1/2)

^{2}= 7/4 *By completing the square

But isn't this is an equation of a sphere??

Shouldn't it just a circle?

Any help is appreciated!