Question

A large circle on a sphere is a circle that forms the intersection of the sphere with a plane through the center of the sphere. Consider the large circle C that arises the intersection sphere x² + y² + z² = 1 and the plane x + y + z = 0.

(a) Express the equations of the specified large circle C using spherical coordinates.

(b) Express the equations of the large circle C using cylindrical coordinates.

(c) Determine a parameterization of C by writing

r (t) = u cos t + v sin t,

where u and v are two orthogonal unit vectors in the plane that cut out C.

(d) Determine the speed and velocity of a particle traveling along the large circle

according to the parameterization in part (c), when the parameter refers to the time.

I need help with c) and d)

Answer 1