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3-1.Vectors
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$\overrightarrow{\mathrm{Q}}$અને,$(2\overrightarrow{\mathrm{Q}}+2\overrightarrow{\mathrm{P}})$ અને $(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$ ના પરિણામી સદિશો વચ્ચેનો કોણ. . . . . . .હશે.
A
$0^{\circ}$
B
$\tan ^{-1} \frac{(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})}{2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}}}$
C
$\tan ^{-1}\left(\frac{P}{Q}\right)$
D
$\tan ^{-1}\left(\frac{2 Q}{P}\right)$
(JEE MAIN-2024)
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
Option $(1)$ is correct
Standard 11
Physics
