A solid spherical shell is centred at the origin. Its inner radius is 5 units and its outer radius is 7 units.
a. (i) Show that a point R(x,y,z) lies in the material of the shell if and only if 25<x2+y2+z2≤49.
b. (ii) A point R moves along the line whose parametric form is R(1+2t,2+3t,3−t), where t∈R. Determine the set of all real values of t for which the point R is inside the shell.
c. (iii) Hence, find the length of the interval of t for which R stays within the shell.