Q101 / 200 · NEET 2003 · Physics

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

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

Solution

$(\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0$ $\begin{aligned} & \Rightarrow A^2-\vec{A} \cdot \vec{B}+\vec{B} \cdot \vec{A}+B^2=0 \\ & \Rightarrow \mathrm{A}=\mathrm{B} \quad(\because \vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{A}) \end{aligned}$

Hence, the correct answer is option: 'B'.

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