Use an ordered parallelogram and a norm constraint

Referred to O, A,B have position vectors $\mathbf a=\mathbf i-\mathbf j+\mathbf k$, $\mathbf b=2\mathbf i+3\mathbf k$. C has position vector $\mathbf c=\lambda\mathbf a+\mu\mathbf b$, where λ,μ are constants.

(i) Find the exact area of triangle OAB.3 marks

(ii) Given that OABC forms a parallelogram, write down λ and μ.2 marks

(iii) Given instead μ=2 and $OC=\sqrt{59}$, find the possible coordinates of C in exact form.4 marks