Question

The angle between vector $(\vec{A})$ and $(\vec{A}-\vec{B})$ 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. $\tan ^{-1}\left(\frac{ B \cos \theta}{ A - B \sin \theta}\right)$

Answer 1

Answer: (C)

Angle between $\vec{ A }$ and $\vec{ B }, \theta=60^{\circ}$
Angle betwenn $\vec{A}$ and $\vec{A}-\vec{B}$
$\tan \alpha=\frac{ B \sin \theta}{ A - B \cos \theta}$
$=\frac{B \sqrt{\frac{3}{2}}}{A-B \times \frac{1}{2} 2}$
$\tan \alpha=\frac{\sqrt{3} B}{2 A-B}$