The vector $c \cdot (b+c) \times (a+b+c)$ is equal to

Three vectors $\vec{a} = \hat{i} + \hat{j}$,$\vec{b} = \hat{j} + \hat{k}$,and $\vec{c} = \hat{k} + \hat{i}$ are given. If three unit vectors are drawn perpendicular to the three planes formed by these vectors,what is the volume of the parallelepiped formed by these unit vectors?

Let $a, b$ and $c$ be distinct positive numbers. If the vectors $a \hat{i} + a \hat{j} + c \hat{k}$,$\hat{i} + \hat{k}$ and $c \hat{i} + c \hat{j} + b \hat{k}$ are coplanar,then $c$ is equal to:

If $[\bar{a} \bar{b} \bar{c}]=3$,then the volume of the parallelepiped with $2 \bar{a}+\bar{b}, 2 \bar{b}+\bar{c}, 2 \bar{c}+\bar{a}$ as coterminus edges is

Let $\bar{a}$ and $\bar{c}$ be unit vectors at an angle $\frac{\pi}{3}$ with each other. If $(\bar{a} \times(\bar{b} \times \bar{c})) \cdot(\bar{a} \times \bar{c})=5$,then $\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]=$

If $[\vec{a} \, \vec{b} \, \vec{c}] = 0$,then: