Question

If θ is the angle between two vectors $\overrightarrow{a}\mathrm{and}\overrightarrow{b},\mathrm{then}\overrightarrow{a}·\overrightarrow{b}\ge 0$ only when
(a) $0<\mathrm{\theta }<\frac{\mathrm{\pi }}{2}$

(b) $0\le \mathrm{\theta }\le \frac{\mathrm{\pi }}{2}$

(c) 0 < θ < π

(d) 0 ≤ θ ≤ π

Answer 1

(b) $0\le \mathrm{\theta }\le \frac{\mathrm{\pi }}{2}$

$$\begin{gathered} \overrightarrow{a}.\overrightarrow{b}\ge 0 \\ \Rightarrow \left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta \ge 0 \\ \Rightarrow \cos \theta \ge 0 \\ \Rightarrow 0\le \theta \le \frac{\mathrm{\pi }}{2} \end{gathered}$$