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

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3-1.Vectors

medium

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

AAre equal to each other in magnitude

BAre not equal to each other in magnitude

CCannot be predicted

DAre equal to each other

(AIPMT-2003) (AIIMS-2012)

Solution

(a) 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.

Standard 11

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medium

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(JEE MAIN-2022)

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

Solution

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