Q63 / 90 · JEE Main 2024 (05 Apr Shift 1) · Physics

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q}+2 \vec{P})$ and $(2 \vec{Q}-2 \vec{P})$ is :

  • A
    $\tan ^{-1} \frac{(2 \vec{Q}-2 \vec{P})}{2 \vec{Q}+2 \vec{P}}$
  • Correct answer
    B
    $0^{\circ}$
  • C
    $\tan ^{-1}(\mathrm{P} / \mathrm{Q})$
  • D
    $\tan ^{-1}(2 \mathrm{Q} / \mathrm{P})$

Solution

$\begin{aligned} & \overrightarrow{\mathrm{R}}=(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})+(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}}) \\ & \overrightarrow{\mathrm{R}}=4 \overrightarrow{\mathrm{Q}} \end{aligned}$ Angle between $\vec{Q}$ and $\vec{R}$ is zero.

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

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