$(b \times c) \times (c \times a) = \dots$

If $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar unit vectors such that $\bar{a} \times (\bar{b} \times \bar{c}) = \frac{\bar{b} + \bar{c}}{\sqrt{2}}$,then the angle between $\bar{a}$ and $\bar{b}$ is:

If $a = 3i - j + 2k,$ $b = 2i + j - k$ and $c = i - 2j + 2k,$ then $(a \times b) \times c$ is equal to

For any vector $r$, the expression $i \times(r \times i) + j \times(r \times j) + k \times(r \times k)$ is equal to:

Let $\vec{a}$ be a non-zero vector. If $\vec{x}=\hat{i} \times(\vec{a} \times \hat{i})$, $\vec{y}=\hat{j} \times(\vec{a} \times \hat{j})-\vec{a}$ and $\vec{z}=\hat{k} \times(\vec{a} \times \hat{k})-\vec{a}$, then $\left[\begin{array}{lll}\vec{x} & \vec{y} & \vec{z}\end{array}\right]=$

$A$ unit vector perpendicular to vector $c$ and coplanar with vectors $a$ and $b$ is