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3-1.Vectors
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The vector sum of two forces is perpendicular to their vector differences. In that case, the force
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
Solution
(a) Let two vectors be $\overrightarrow A $ and $\overrightarrow B $ then
$(\overrightarrow A + \overrightarrow B ).(\overrightarrow A – \overrightarrow B ) = 0$
$\overrightarrow A \;.\;\overrightarrow A – \overrightarrow B \;.\;\overrightarrow B + \overrightarrow B \;.\;\overrightarrow A – \overrightarrow B \;.\;\overrightarrow B = 0$
${A^2} – {B^2} = 0$ $⇒$ ${A^2} = {B^2}$
$\therefore \;\;A = B$
Standard 11
Physics
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