Question

If $\theta$ is the angle between two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ then $3.6>0$ only when then $\overrightarrow{a}.\overrightarrow{b}\ge 0$ only when

• A. $0<\theta <\frac{\pi }{2}$
• B. $0\le \theta \le \frac{\pi }{2}$
• C. $0<\theta <\pi$
• D. $0\le \theta \le \pi$

Answer 1

The correct option is B $0\le \theta \le \frac{\pi }{2}$

$\overline{a}.\overline{b}=|\overline{a}||\overline{b}|cos\theta$

$\therefore \overline{a}.\overline{b}\ge 0$ if $cos\theta \ge 0\Rightarrow 0\le \theta \le \frac{\pi }{2}$

$\therefore$ Answer is $\left(B\right)$