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Newton's Laws of Motion — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsNewton's Laws of Motion1 Mark
MCQ
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
  • ✓
    Are equal to each other
✓

Answer

Correct option: D.
Are equal to each other
(a) Let two vectors be $\vec{A}$ and $\vec{B}$ then
$\vec{A}\vec{B} \cdot (\vec{A}\vec{B})=0$
$\vec{A} \cdot \vec{A}-\vec{B} \cdot \vec{B}+\vec{B} \cdot \vec{A}\vec{B}\cdot \vec{B}=0 $
$A^2-B^2=0 \Rightarrow A^2=B^2 \therefore A=B$

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