Very simple

Let the $2$ vectors be $\vec{a}$ and $\vec{b}$ and the angle between them be $\theta$ . Assume that the magnitude of the $2$ vectors is non-zero and $\theta$ is in principal range, i.e., $\theta \in [0,\pi]$ . Now, given that ---->

$\vec{a} \centerdot \vec{b} = \vec{a} \times \vec{b}$

$\implies |\vec{a}||\vec{b}| \cos \theta = |\vec{a}||\vec{b}| \sin \theta$

$\implies \cos \theta = \sin \theta$

$\implies \tan \theta = 1 \implies \boxed{\theta = 45^{\circ}}$