The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
Are equal to each other in magnitude
Are not equal to each other in magnitude
Cannot be predicted
Are equal to each other
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
If two vectors are perpendicular then their dot product must be equal to zero. According to problem
$(\overrightarrow A + \overrightarrow B ).(\overrightarrow A - \overrightarrow B ) = 0$
$⇒$$\overrightarrow A .\overrightarrow A - \overrightarrow A .\overrightarrow B + \overrightarrow B .\overrightarrow A - \overrightarrow B .\overrightarrow B = 0$
$⇒$ ${A^2} - {B^2} = 0$
$⇒$ ${A^2} = {B^2}$
$\therefore $ $A = B$ i.e. two vectors are equal to each other in magnitude.
$(\overrightarrow A + \overrightarrow B ).(\overrightarrow A - \overrightarrow B ) = 0$
$⇒$$\overrightarrow A .\overrightarrow A - \overrightarrow A .\overrightarrow B + \overrightarrow B .\overrightarrow A - \overrightarrow B .\overrightarrow 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.
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