Question

If $|{\overset{\rightarrow}{V}}_{1} + {\overset{\rightarrow}{V}}_{2}| = |{\overset{\rightarrow}{V}}_{1} - {\overset{\rightarrow}{V}}_{2}|$and $V_{2}$ is finite, then

• A. $V_{1}$ is parallel to $V_{2}$
• B. ${\overset{\rightarrow}{V}}_{1} = {\overset{\rightarrow}{V}}_{2}$
• C. $V_{1}$ and $V_{2}$ are mutually perpendicular
• D. $|{\overset{\rightarrow}{V}}_{1}| = |{\overset{\rightarrow}{V}}_{2}|$

Answer 1

Answer: (C)

$V_{1}$ and $V_{2}$ are mutually perpendicular

Answer 2

According to problem $|{\overrightarrow{V}}_{1} + {\overrightarrow{V}}_{2}|\mspace{6mu} = \mspace{6mu}|{\overrightarrow{V}}_{1} - {\overrightarrow{V}}_{2}|$

⇒ $|{\overrightarrow{V}}_{\text{net}}|\mspace{6mu} = \mspace{6mu}|V^{{\overrightarrow{'}}_{\text{net}}}$

So $V_{1}$ and $V_{2}$ will be mutually perpendicular.