Remove a parallel component from an area calculation

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

(i) Given the area of OAC is $\sqrt{126}$, find μ.4 marks

(ii) Given instead μ=4 and $OC=5\sqrt3$, find the possible coordinates of C.4 marks