$(\hat{i} \times \hat{j}) \cdot [(\hat{j} \times \hat{k}) \times (\hat{k} \times \hat{i})]$

If $\bar{a}+\bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a}$ are coterminous edges of a parallelepiped,then its volume is

If $a, b$ and $c$ are non-coplanar vectors and the four points with position vectors $2a+3b-c$,$a-2b+3c$,$3a+4b-2c$ and $ka-6b+6c$ are coplanar,then $k=$

Let $a=\hat{i}+2 \hat{j}-\hat{k}$ and $b=\hat{i}+\hat{j}+\hat{k}$. If $p$ is a unit vector such that $[a b p]$ is maximum,then $p=$

Let $a = \hat{i} - 2\hat{j} + 3\hat{k}$ and $b = 2\hat{i} + \hat{j} + \hat{k}$. If $c$ is a unit vector such that $[a \ b \ c]$ is maximum,then $c =$

Let $\vec{b} = -\hat{i} + 4\hat{j} + 6\hat{k}$ and $\vec{c} = 2\hat{i} - 7\hat{j} - 10\hat{k}$. If $\vec{a}$ is a unit vector and the scalar triple product $[\vec{a} \ \vec{b} \ \vec{c}]$ has the greatest value,then $\vec{a}$ is equal to: