Which of the following is a true statement?

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.

If $a, b$ and $c$ are non-zero vectors such that $a \times b = c$ and $b \times c = a$,then $a \times c$ is

Statement $(A)$ : If $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{c}$,then $\vec{a} \times (\vec{b} \times \vec{c}) = 0$.
Reason $(R)$ : If $\vec{b}$ is perpendicular to $\vec{c}$,then $\vec{b} \times \vec{c} = 0$.

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

If $a = i + j + k$,$b = i + j$,$c = i$ and $(a \times b) \times c = \lambda a + \mu b$,then $\lambda + \mu = \dots$