Question

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

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

Answer 1

Answer: (A)

Are equal to each other in magnitude

Answer 2

If two vectors are perpendicular then their dot product must be equal to zero. According to problem

$(\overset{\rightarrow}{A} + \overset{\rightarrow}{B}).(\overset{\rightarrow}{A} - \overset{\rightarrow}{B}) = 0$⇒$\overset{\rightarrow}{A}.\overset{\rightarrow}{A} - \overset{\rightarrow}{A}.\overset{\rightarrow}{B} + \overset{\rightarrow}{B}.\overset{\rightarrow}{A} - \overset{\rightarrow}{B}.\overset{\rightarrow}{B} = 0$

⇒$A^{2} - B^{2} = 0$⇒$A^{2} = B^{2}$

$\therefore$ $A = B$ i.e. two vectors are equal to each other in magnitude.