Question

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

• A. are not equal to each other in magnitude
• B. are parallel
• C. are perpendicular
• D. are equal to each other in magnitude

Answer 1

The correct option is D are equal to each other in magnitude

Let the vectors be $\overrightarrow{A}$ and $\overrightarrow{B}$
($\overrightarrow{A}$ + $\overrightarrow{B}$).($\overrightarrow{A}$ - $\overrightarrow{B}$) = 0
$\therefore \overrightarrow{A}$.$\overrightarrow{A}$ + $\overrightarrow{B}$. $\overrightarrow{A}$ - $\overrightarrow{A}$ . $\overrightarrow{B}$ - $\overrightarrow{B}$. $\overrightarrow{B}=0$
$\therefore |A{|}^2+\text{|A||B| cos}\theta -\text{|A||B| cos}\theta -|B{|}^2=0$
$\therefore |A|=|B|$