1.2
A large circle on a sphere is a circle that forms theintersection of the sphere with a plane through the center of thesphere. Consider the large circle C that arises the intersectionsphere x2 + y2 + z2 = 1 and theplane x + y + z = 0.
(a) Express the equations of the specified large circle C usingspherical coordinates.
(b) Express the equations of the large circle C usingcylindrical 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 thatcut out C.
(d) Determine the speed and velocity of a particle travelingalong the large circle
according to the parameterization in part (c), when theparameter refers to the time.
