Question

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

• A. are equal to each other
• B. are equal to each other in magnitude
• C. are not equal to each other in magnitude
• D. cannot be predicted

Answer 1

Answer: (B)

are equal to each other in magnitude

Answer 2

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