If $\vec{a}$ and $\vec{b}$ are perpendicular,then $\vec{a} \times(\vec{a} \times(\vec{a} \times(\vec{a} \times \vec{b})))$ is equal to

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

Let $\vec{a}=3 \hat{i}+\hat{j}$ and $\vec{b}=\hat{i}+2 \hat{j}+\hat{k}$. Let $\vec{c}$ be a vector satisfying $\vec{a} \times(\vec{b} \times \vec{c})=\vec{b}+\lambda \vec{c}$. If $\vec{b}$ and $\vec{c}$ are non-parallel,then the value of $\lambda$ is.

Which of the following statements is true regarding the vector triple product $(a \times b) \times c$?

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and $(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3}|\vec{b}| |\vec{c}| \vec{a}$. If $\theta$ is the angle between vectors $\vec{b}$ and $\vec{c}$,then a value of $\sin \theta$ is:

If $a=(1,2,3), b=(2,-1,1), c=(3,2,1)$ and $a \times(b \times c)=\alpha a+\beta b+\gamma c$,then