A moving point P(t,2t,t+1) depends on the real parameter t.
a. (i) Obtain, in simplest form, an expression for the square of the distance of P from the origin in terms of t.
b. (ii) For what values of t does the point P lie strictly inside the sphere of radius 5 centred at the origin?
c. (iii) For what value(s) of t does P lie on the surface of the same sphere?