Question

The magnitude of scalar product of two vectors is $8$ and of vector product is $8\sqrt{3}$. The angle between them is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

Answer: (B), (C)

The correct options are
B ${120}^{\circ }$
C ${60}^{\circ }$

$\left|\begin{array}{c}\overrightarrow{A}.\overrightarrow{B}\end{array}\right|=AB\left|\begin{array}{c}cos\theta \end{array}\right|=8$

$\left|\begin{array}{c}\overrightarrow{A}\times \overrightarrow{B}\end{array}\right|=AB\left|\begin{array}{c}sin\theta \end{array}\right|=8\sqrt{3}$

$\Rightarrow \left|\begin{array}{c}tan\theta \end{array}\right|=\frac{8\sqrt{3}}{8}=\sqrt{3}\Rightarrow \theta ={60}^{\circ },{120}^{\circ }$