Question

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be the three vectors having magnitudes $1,5$ and $3$ , respectively, such that the angle between $\vec{a}$ and $\vec{b}$ is $\theta$ and $\vec{a} \times(\vec{a} \times \vec{b})=\vec{c}$. Then $\tan \theta$ is equal to

• A. 0
• B. $2 / 3$
• C. $3 / 5$
• D. $3 / 4$

Answer 1

Answer: (D)

$\vec{a} \times(\vec{a} \times \vec{b})=\vec{c}$
$ \Rightarrow|\vec{a}||\vec{a} \times \vec{b}|=|\vec{c}| $
$(\because \vec{a} \perp(\vec{a} \times \vec{b}))$
$1(1 \times 5) \sin \theta=3 $
$\Rightarrow \sin \theta=\frac{3}{5} $
$\Rightarrow \tan \theta=\frac{3}{4} .$