What will be the volume of the parallelepiped whose coterminous edges are given by the vectors $a = i - j + k$,$b = i - 3j + 4k$,and $c = 2i - 5j + 3k$?

If the vectors $2 \hat{i}+3 \hat{j}+4 \hat{k}$,$2 \hat{i}+\hat{j}-\hat{k}$ and $\lambda \hat{i}-\hat{j}+2 \hat{k}$ are coplanar,then the value of $\lambda$ is:

If $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$,$\vec{b} = 2\hat{i} + 3\hat{j} - \hat{k}$,and $\vec{c} = \lambda\hat{i} + \hat{j} + (2\lambda - 1)\hat{k}$ are coplanar vectors,then $\lambda = . . . .$

If the vectors $2i - j + k$,$i + 2j - 3k$,and $3i + \lambda j + 5k$ are coplanar,then $\lambda = $

If four distinct points with position vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are coplanar,then $[\vec{a} \vec{b} \vec{c}]$ is equal to

If $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ are non-zero coplanar vectors,then $[2 \overrightarrow{a}-\overrightarrow{b} \quad 3 \overrightarrow{b}-\overrightarrow{c} \quad 4 \overrightarrow{c}-\overrightarrow{a}]$ is