If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$,$\vec{b} = \hat{i} + \hat{j}$,$\vec{c} = \hat{i}$ and $(\vec{a} \times \vec{b}) \times \vec{c} = \lambda \vec{a} + \mu \vec{b}$,then $\lambda + \mu$ is equal to :-

Let $a, b$ and $c$ be non-zero vectors such that $(a \times b) \times c = \frac{1}{3}|b||c|a$. If $\theta$ is the acute angle between the vectors $b$ and $c$,then $\sin \theta$ equals

Let $\vec{v}$ be a unit vector which follows the equation $\vec{v} \times \vec{b} = \vec{c}$. Also,$|\vec{b}| = 2$ and $|\vec{c}| = \sqrt{3}$. Then,which of the following is true?

$\hat{a}, \hat{b}$,and $\hat{c}$ are three unit vectors such that $\hat{a} \times(\hat{b} \times \hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c})$. If $\hat{b}$ is not parallel to $\hat{c}$,then the angle between $\hat{a}$ and $\hat{b}$ is

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three vectors having magnitudes $1, 1$ and $2$ respectively. If $\bar{a} \times(\bar{a} \times \bar{c})+\bar{b}=\bar{0}$,then the acute angle between $\bar{a}$ and $\bar{c}$ is

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors having magnitudes $1, 1$ and $2$ respectively. If $\vec{a} \times (\vec{a} \times \vec{c}) + \vec{b} = \vec{0}$, then the acute angle between $\vec{a}$ and $\vec{c}$ is