Question

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

• A. Cannot be predicted
• B. Are equal to each other
• C. Are equal to each other in magnitude
• D. Are not equal to each other in magnitude

Answer 1

The correct option is C Are equal to each other in magnitude

$\overrightarrow{P}$ $=$ vector sum $=$ $\overrightarrow{A}+\overrightarrow{B}$

$\overrightarrow{Q}$ $=$ vector vector differences $=$ $\overrightarrow{A}-\overrightarrow{B}$

Since $\overrightarrow{P}$ and $\overrightarrow{P}$ are perpendicular.

$\therefore \overrightarrow{P}.\overrightarrow{Q}=0$

$\Rightarrow (\overrightarrow{A}+\overrightarrow{B}).(\overrightarrow{A}-\overrightarrow{B})=0\Rightarrow A^2=B^2$

$\Rightarrow \left|A\right|=\left|B\right|$