If $\left|{\overrightarrow{V}}_1+{\overrightarrow{V}}_2\right|=\left|{\overrightarrow{V}}_1-{\overrightarrow{V}}_2\right|\text{ and }{V}_2$ is finite, then

According to problem $\left|{\overrightarrow{V}}_1+{\overrightarrow{V}}_2\right|=\left|{\overrightarrow{V}}_1-{\overrightarrow{V}}_2\right|$

$\Rightarrow \sqrt{V_1^2+V_2^2+2V_1{V}_2\cos \theta }=\sqrt{V_1^2+V_2^2-2V_1{V}_2\cos \theta }$

$\Rightarrow \cos \theta =0$

$\Rightarrow \theta ={90}^0$

$\text{ So }{V}_1\text{ and }{V}_2\text{ will be mutually perpendicular. }$

$\begin{array}{l}Also,\left|{\overrightarrow{V}}_{\text{net }}\right|=\left|{\overrightarrow{V}}_{\text{net }}^{\mathrm{\prime }}\right|\\ \end{array}$