MCQ
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
    $\tan ^{-1}\left(\frac{{A}}{0.7 {B}}\right)$
  • $\tan ^{-1}\left(\frac{\sqrt{3} {B}}{2 {A}-{B}}\right)$
  • D
    $\tan ^{-1}\left(\frac{{B} \cos \theta}{{A}-{B} \sin \theta}\right)$

Answer

Correct option: C.
$\tan ^{-1}\left(\frac{\sqrt{3} {B}}{2 {A}-{B}}\right)$
c
Angle between $\overrightarrow{{A}}$ and $\overrightarrow{{B}}, \theta=60^{\circ}$

Angle betwenn $\overrightarrow{{A}}$ and $\overrightarrow{{A}}-\overrightarrow{{B}}$

$\tan \alpha=\frac{B \sin \theta}{A-B \cos \theta}$

$=\frac{B \sqrt{\frac{3}{2}}}{A-B \times \frac{1}{2} 2}$

$\tan \alpha=\frac{\sqrt{3} B}{2 A-B}$

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