Please provide the full solution thanks

3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the uppermost pole. With its spherical angular positions parametrically defined by 0(t) = t and o(t) = 24t, the particle's path can be defined r(t) = sin(0(t)) cos(6(t)) 2 + sin(0(t)) sin(o(t)) 3 + cos(0(t)) k , te [37/2, 27]. Compute the work done by the constant vector field F(x, y, z) = 1 k in moving the particle along this path. O