Vector Algebra

Let $\bar{a}, \bar{b}, \bar{c}$ be unit vectors such that $\bar{a}$ is perpendicular to the plane of $\bar{b}$ and $\bar{c}$. If the angle between $\bar{b}$ and $\bar{c}$ is $\dfrac{\pi}{3}$, then $|\bar{a} + \bar{b} + \bar{c}| =$