Question

Choose the correct answer
If $\theta$ is the angle between two vectors a and b, then $a.b\ge 0$ only when
a) $0<\theta <\frac{\pi }{2}$
b) $0\le \theta <\frac{\pi }{2}$
c) $0<\theta <\pi$
d) $0\le \theta \le \pi$

Answer 1

It is given that $a.b\ge 0$
We know that $a.b=|a||b|cos\theta \ge 0\Rightarrow cos\theta \ge 0$, [|a| and |b| are positive]
$\Rightarrow 0\le \theta \le \frac{\pi }{2}$