Vector Algebra

If $\hat{\mathbf{a}} \cdot \hat{\mathbf{b}}=0$, where $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ are unit vectors and the unit vector $\hat{\complement}$ is inclined at an angle $\theta$ to both $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$. If $\hat{\mathbf{c}}=m \hat{\mathbf{a}}+n \hat{\mathbf{b}}+p(\hat{\mathbf{a}} \times \hat{\mathbf{b}})$, where, $m, n, p \in R$, then