Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces  Also name the triangle formed by the forces as sides

  • A

    $120^°$ equilateral triangle

  • B

    $60^°$ equilateral triangle

  • C

    $120^°, 30^°, 30^° $ an isosceles triangle

  • D

    $120^°$ an obtuse angled triangle

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  • [AIIMS 2019]
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The resultant of two vectors $A$ and $B$ is perpendicular to the vector $A$ and its magnitude is equal to half the magnitude of vector $B$. The angle between $A$ and $B$ is ....... $^o$

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Statement $I :$Two forces $(\overrightarrow{{P}}+\overrightarrow{{Q}})$ and $(\overrightarrow{{P}}-\overrightarrow{{Q}})$ where $\overrightarrow{{P}} \perp \overrightarrow{{Q}}$, when act at an angle $\theta_{1}$ to each other, the magnitude of their resultant is $\sqrt{3\left({P}^{2}+{Q}^{2}\right)}$, when they act at an angle $\theta_{2}$, the magnitude of their resultant becomes $\sqrt{2\left({P}^{2}+{Q}^{2}\right)}$. This is possible only when $\theta_{1}<\theta_{2}$.

Statement $II :$ In the situation given above. $\theta_{1}=60^{\circ} \text { and } \theta_{2}=90^{\circ}$ In the light of the above statements, choose the most appropriate answer from the options given below

  • [JEE MAIN 2021]