3. Parametrized Surfaces. When we converted the coordinates and equations from rectangular coordinates to spherical coordinates, we created a parametrization of a surface. This parameterization was in two variables (not one). (a) Using spherical coordinates, write a vector-valued function in terms of u (which will replace θ and v which will replace φ for a unit sphere( ρ = 1). Remember this will require you to find equations for x, y, and z, and express your answer as r(u, v) = x(u, v)i + y(u, v)j + z(u, v)k. Give the parameterized surface equation for a sphere of radius 4.
3. Parametrized Surfaces. When we converted the coordinates and equations from rectangular coordinates to spherical
coordinates, we created a parametrization of a surface. This parameterization was in two variables (not one).
(a) Using spherical coordinates, write a
replace φ for a unit sphere( ρ = 1). Remember this will require you to find equations for x, y, and z, and express
your answer as r(u, v) = x(u, v)i + y(u, v)j + z(u, v)k. Give the parameterized surface equation for a sphere of
radius 4.
(b) Graph the sphere of radius 4 using your parameterization. You can do this by going to ”Select Graph”, parametric
surface.
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