If θ is the angle between two vectors

Let $\theta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$.

Then, without loss of generality, $\vec{a}$ and $\vec{b}$ are non-zero vectors so that $|\vec{a}|$ and $|\vec{b}|$ are positive.

It is known that $\vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta$.

$\therefore \vec{a} \cdot \vec{b} \geq 0$

$\Rightarrow|\vec{a}| \vec{b} \mid \cos \theta \geq 0$

$\Rightarrow \cos \theta \geq 0$                                     $[|\vec{a}|$ and $|\vec{b}|$ are positive $]$

$\Rightarrow 0 \leq \theta \leq \frac{\pi}{2}$

Hence, $\vec{a} \cdot \vec{b} \geq 0$ when $0 \leq \theta \leq \frac{\pi}{2}$.

The correct answer is B.