Question

The magnitude of scalar product of two vectors is 8 and that 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

The correct option is B ${60}^{\circ }$

Let the two vectors be $\overrightarrow{a}$ and $\overrightarrow{b}$ whose magnitude is $a$ and $b$ respectively
As per the question we have,
$\text{ab cos}\theta =8....\left(1\right)$
And, $\text{ab sin}\theta =8\sqrt{3}....\left(2\right)$
On, $\left(2\right)÷\left(1\right)$ we get
$tan\theta =\sqrt{3}$
$\theta ={60}^{\circ }$