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JEE Mains · Physics · STD 11 - 3.1 vectors

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

  1. A Statement\(-I\) is false but Statement\(-II\) is true
  2. B Both Statement\(-I\) and Statement\(-II\) are true
  3. C Statement\(-I\) is true but Statement\(-II\) is false
  4. D Both Statement\(-I\) and Statement\(-II\) are false.
Verified Solution

Answer & Solution

Correct Answer

(B) Both Statement\(-I\) and Statement\(-II\) are true

Step-by-step Solution

Detailed explanation

\(\overrightarrow{{A}}=\overrightarrow{{P}}+\overrightarrow{{Q}}\) \(\overrightarrow{{B}}=\overrightarrow{{P}}-\overrightarrow{{Q}} \quad \overrightarrow{{P}} \perp \overrightarrow{{Q}}\) \(|\overrightarrow{{A}}|=|\overrightarrow{{B}}|=\sqrt{{P}^{2}+{Q}^{2}}\)…
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