If is the angle between two vectors a and b , then a . b 0 only w… - Vidyadip

Question

If $\theta$ is the angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\vec{\text{a}}.\vec{\text{b}}\geq0$ only when:

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

✓

Answer

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

Solution:

$\vec{\text{a}}.\vec{\text{b}}\geq0$

$\Rightarrow|\vec{\text{a}}|\big|\vec{\text{b}}\big|\cos\theta\geq0$

$\Rightarrow\cos\theta\geq0$

$\Rightarrow0\leq\theta\leq\frac{\pi}{2}$

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