(a) Substituting for m and n to get 2(i - j) + 2i + 3j - r = 0 and solving for r to get r = 4i + j
Thus |r| = $\sqrt{4^2+1^2}$ = $\sqrt{17}$ = 4.1231

(b)(i) Given that S = 3t - $\frac{r^3}{3}$ + 9, they took the derivative of S with respect to t and equated to zero to obtain $\frac{d_s}{d_t}$ = 3 - t${}^2$ = 0
Solve to get t = $\sqrt{3}$ = 1.7321 seconds

(b)(ii) Substituting for (t), the distance covered is S = 3(1.7321) - $\frac{(1.7321{)}^3}{3}$ + 9
Therefore; 5.1963 - 1.732198389 + 9
= 12.4641 metres