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3-1.Vectors
hard
The angle between vector $(\overrightarrow{{A}})$ and $(\overrightarrow{{A}}-\overrightarrow{{B}})$ is :
A
$\tan ^{-1}\left(\frac{-\frac{{B}}{2}}{{A}-{B} \frac{\sqrt{3}}{2}}\right)$
B
$\tan ^{-1}\left(\frac{{A}}{0.7 {B}}\right)$
C
$\tan ^{-1}\left(\frac{\sqrt{3} {B}}{2 {A}-{B}}\right)$
D
$\tan ^{-1}\left(\frac{{B} \cos \theta}{{A}-{B} \sin \theta}\right)$
(JEE MAIN-2021)
Solution
Angle between $\overrightarrow{{A}}$ and $\overrightarrow{{B}}, \theta=60^{\circ}$
Angle betwenn $\overrightarrow{{A}}$ and $\overrightarrow{{A}}-\overrightarrow{{B}}$
$\tan \alpha=\frac{B \sin \theta}{A-B \cos \theta}$
$=\frac{B \sqrt{\frac{3}{2}}}{A-B \times \frac{1}{2} 2}$
$\tan \alpha=\frac{\sqrt{3} B}{2 A-B}$
Standard 11
Physics
