question_answer

If \[|{{\overrightarrow{V}}_{1}}+{{\overrightarrow{V}}_{2}}|\,=\,|{{\overrightarrow{V}}_{1}}-{{\overrightarrow{V}}_{2}}|\]and \[{{V}_{2}}\] is finite, then      [CPMT 1989]

A)                 \[{{V}_{1}}\] is parallel to \[{{V}_{2}}\]  

B)                                 \[{{\overrightarrow{V}}_{1}}={{\overrightarrow{V}}_{2}}\]         

C)                 \[{{V}_{1}}\] and \[{{V}_{2}}\] are mutually perpendicular

D)                                 \[|{{\overrightarrow{V}}_{1}}|\,=\,|{{\overrightarrow{V}}_{2}}|\]

Correct Answer: C

Solution :

                    According to problem \[|{{\vec{V}}_{1}}+{{\vec{V}}_{2}}|\ =\ |{{\vec{V}}_{1}}-{{\vec{V}}_{2}}|\] Þ \[|{{\vec{V}}_{\text{net}}}|\ =\ |{{\vec{{V}'}}_{\text{net}}}|\]                 So \[{{V}_{1}}\] and \[{{V}_{2}}\] will be mutually perpendicular.