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 $45°$.