Since the scalar product of two vectors is equal to the magnitude of their vector product,
\[\overrightarrow{A}.\overrightarrow{B}=|\overrightarrow{A}×\overrightarrow{B}|\]
\[AB\cos\theta=AB\sin\theta\]
\[1=\frac{\sin\theta}{\cos\theta}\]
\[\tan\theta=1\]
\[\therefore\theta=45°\]
Hence, the angle between the two vectors is $45°$.