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Motion in a Plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane3 Marks
Question
  1. What can be the maximum and minimum values of $(\vec{\text{A}}+\vec{\text{B}})$ and $(\vec{\text{A}}-\vec{\text{B}})?$
  2. If two vectors of equal magnitude added to each other gives magnitude of one of them. What is the angle between them?
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Answer

Minimum value $=(\vec{\text{A}}-\vec{\text{B}})$ Maximum value $=(\vec{\text{A}}+\vec{\text{B}})$
Let vector is $A$, then It is given that two vectors of equal magnitude added to each other gives magnitude of one of them, i.e. $\sqrt{\text{A}^2+\text{A}^2+2\text{A}.\text{A}\cos\theta}=\text{A}$ Squaring on both sides, we get $\text{A}^2(1+2\cos\theta)=\text{A}^2$
$\Rightarrow\ \cos\theta=\frac{-1}{2}$ 
$\Rightarrow\ \theta=120^\circ$

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