Question

If $|\overline{a}+\overline{b}|<|\overline{a}-\overline{b}|$ then the angle between the vectors $\overline{a}$ and $\overline{b}$ is

• A. Acute angle
• B. Obtuse angle
• C. Right angle
• D. ${45}^o$

Answer 1

The correct option is B Obtuse angle

$|\overrightarrow{a}+\overrightarrow{b}|<|\overrightarrow{a}-\overrightarrow{b}|$

$\Rightarrow {\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2+2\overrightarrow{a}.\overrightarrow{b}<{\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2-2\overrightarrow{a}.\overrightarrow{b}=1$

$\Rightarrow 4\overrightarrow{a}.\overrightarrow{b}<0$

$\Rightarrow 4\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta <0$

$\therefore \cos \theta <0$

$\therefore \theta \in (\frac{\pi }{2},\frac{3\pi }{2})$