What Is the Equation of a Sphere in Spherical Coordinates?

[Philosophaie]

Looking for the equation in spherical coordinates and the spherical equation with the unit vectors:
Frr + FӨӨ + FØØ = constant

The equation is:

x^2 + y^2 + z^2 = r^2

is the equation for a sphere radius = r centered at the origin. What is the cartesian equation?

x*x + y*y + z*z = r ?

What is the sphere in spherical coordianates?

r*cosӨ*sinØ*r + r*sinӨ*sinØ /(r*sin)*Ө + r*cosØ/r*Ø = Constant ?

or

r*cosӨ*sinØ*r + sinӨ*Ө + cosØ*Ø =Constant ?

 

[HallsofIvy]

Looking for the equation in spherical coordinates and the spherical equation with the unit vectors:
Frr + FӨӨ + FØØ = constant

The equation is:

x^2 + y^2 + z^2 = r^2

is the equation for a sphere radius = r centered at the origin. What is the cartesian equation?

x*x + y*y + z*z = r ?

What you gave before WAS the Cartesian equation. I can't make any sense of the equation you give here because the left side of the equation is a vector while the right side is a number.

What is the sphere in spherical coordianates?

r*cosӨ*sinØ*r + r*sinӨ*sinØ /(r*sin)*Ө + r*cosØ/r*Ø = Constant ?

or

r*cosӨ*sinØ*r + sinӨ*Ө + cosØ*Ø =Constant ?

The equation of the sphere you gave before, with center at (0,0,0) and radius r, in spherical coordinates is, of course, $\rho= r$.
Again, your "vector equation" is setting a vector equal to a number.