In the circus, a lion has been trained to jump through a ring of fire that has a circumference of 8 yards. What is the rings area?

Find a parametrization for the curve「and determine the work done on a particle moving along γ in r3 through the force field f: r^3--r^3'where f(x,y,z) = (1,-x,z) and (a) im (γ) is the line segment from (0,0,0) to (1,2,1) (b) im (γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) im (γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)