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Question:
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If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$, then $\vec{a} \cdot \vec{b} \geq 0$ only when
(a) $0 < \theta < \frac{\pi}{2}$
(b) $0 \leq \theta \leq \frac{\pi}{2}$
(c) $0 < \theta < \pi$
(d) $0 \leq \theta \leq \pi$
(a) $0 < \theta < \frac{\pi}{2}$
(b) $0 \leq \theta \leq \frac{\pi}{2}$
(c) $0 < \theta < \pi$
(d) $0 \leq \theta \leq \pi$
Solution:
2568 Upvotes
Verified Answer
$$
\vec{a} \cdot \vec{b} \geq 0 \Rightarrow|\vec{a}||\vec{b}| \cos \theta \geq 0
$$
Now $|\vec{a}|=+$ ve, $|\vec{b}|=+$ ve $\quad \Rightarrow \cos \theta \geq$
$\therefore \quad 0 \leq \theta \leq \frac{\pi}{2} \quad$ Option $(b)$ is correct.
\vec{a} \cdot \vec{b} \geq 0 \Rightarrow|\vec{a}||\vec{b}| \cos \theta \geq 0
$$
Now $|\vec{a}|=+$ ve, $|\vec{b}|=+$ ve $\quad \Rightarrow \cos \theta \geq$
$\therefore \quad 0 \leq \theta \leq \frac{\pi}{2} \quad$ Option $(b)$ is correct.
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