Vector Algebra

Let $\mathbf{c}$ be a vector coplanar with the unit vectors $\mathbf{a}, \mathbf{b}$ and let $\mathbf{d}$ be the unit vector perpendicular to $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$. If $[\mathbf{a} \mathbf{b} \mathbf{d}] \mathbf{c}-[\mathbf{a} \mathbf{b} \mathbf{c}] \mathbf{d}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and the angle between $\mathbf{a}$ and $\mathbf{b}$ is $30^{\circ}$, then $|\mathbf{c}|=$