Physics - Vectors Question with Solution | TestHub

Using parallelogram law of vector addition, the formula can be written as

${\mathrm{A}}_{\mathrm{net}}=\sqrt{{{\mathrm{A}}_1}^2+{{\mathrm{A}}^2}_2+2{\mathrm{A}}_1{\mathrm{A}}_2\cos \theta }$

The data given is 

$\left|\overrightarrow{A_1}\right|=A, \left|\overrightarrow{A_2}\right|=\frac{A}{2}$

Since the vectors are perpendicular $\cos 90°=0$

$\Rightarrow {\mathrm{F}}_{\mathrm{net}}=\sqrt{{\mathrm{A}}^2+\frac{{\mathrm{A}}^2}{4}}$$=\frac{\sqrt{5}\mathrm{A}}{2}$