The angle between vector overrightarrow Q and the resultant of (2 overrightarrow Q +2 overrightarrow P ) and (2 overrightarrow Q -2 overrightarrow P ) is:

tan -1 frac (2 overrightarrow Q -2 overrightarrow P ) 2 overrightarrow Q +2 overrightarrow P

Physics · Vectors and Scalars

JEE Main 2024 — 5 April, Shift 1 — Question 35

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

Option A:
$0^{\circ}$
Correct
Option B:
$\tan ^{-1} \frac{(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})}{2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}}}$
Option C:
$\tan ^{-1}\left(\frac{P}{Q}\right)$
Option D:
$\tan ^{-1}\left(\frac{2 Q}{P}\right)$

Answer: A

Step-by-step solution

$\overrightarrow{\mathrm{R}}=(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})+(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$

$\overrightarrow{\mathrm{R}}=4 \overrightarrow{\mathrm{Q}}$

Angle between $\vec{Q}$ and $\vec{R}$ is zero

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 1
Subject: Physics
Chapter: Vectors and Scalars
Topic: Product of Vectors and Applications