Motion in a Plane

Let $\theta$ be the angle which the path of the particle makes with the x-axis.
The particle moves along the straight line from (0, 0) to $(\sqrt{3}, 3)$.
$\tan\theta = \dfrac{y}{x} = \dfrac{3}{\sqrt{3}}$
$\tan\theta = \sqrt{3}$
$\theta = \tan^{-1}(\sqrt{3}) = 60^\circ$

$|\vec{A} \times \vec{B}| = AB\sin\theta$ and $\vec{A}\cdot\vec{B} = AB\cos\theta$
Given $|\vec{A} \times \vec{B}| = \sqrt{3}\,(\vec{A}\cdot\vec{B})$
$\Rightarrow AB\sin\theta = \sqrt{3}\,AB\cos\theta$
$\Rightarrow \tan\theta = \sqrt{3}$
$\Rightarrow \theta = 60^\circ$