Expand a cross product for an area ratio

Referred to O, $OA=\mathbf a$, $OB=\mathbf b$, with OA perpendicular to OB. C,D lie on AB such that $AC:CB=\lambda:(1-\lambda)$ and $AD:DB=\mu:(1-\mu)$, where $0<\lambda<\mu<1$.

(i) Find OC in terms of a,b,λ and OD in terms of a,b,μ. By considering their vector product, show that the area of triangle OCD is $\frac12(\mu-\lambda)|\mathbf a\times\mathbf b|$.5 marks

Now $\mathbf a=2\mathbf i+3\mathbf j-\mathbf k$, $\mathbf b=-\mathbf i+2\mathbf j+4\mathbf k$ and AC:CD:DB=2:3:4.

(ii) Use (i) to calculate the exact area of triangle OCD.3 marks