If a⃗ and b⃗ are two non-zero vectors such that |a⃗ × b⃗| = a⃗ · b⃗, find the angle between a⃗ and…

$|\vec a\times\vec b| = |\vec a||\vec b|\sin\theta$ and $\vec a\cdot\vec b = |\vec a||\vec b|\cos\theta$. Given $|\vec a\times\vec b| = \vec a\cdot\vec b$: $|\vec a||\vec b|\sin\theta = |\vec a||\vec b|\cos\theta$ Since $\vec a, \vec b$ are non-zero, $\tan\theta = 1$, so $\theta = \frac{\pi}{4}$.