Vector Algebra

For two vectors $\vec{P}$ and $\vec{Q}$, $\vec{P} \cdot \vec{Q} = |\vec{P} \times \vec{Q}|$
The magnitude of $\vec{R} = \vec{P} + \vec{Q}$ is ($\cos 45^\circ = \dfrac{1}{\sqrt{2}}$) ?