$[\hat{i}-\hat{j}, \hat{j}-\hat{k}, \hat{k}-\hat{i}]$ 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

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 $k=$

If $\vec{a}=\alpha \hat{i}+\beta \hat{j}+3 \hat{k}$,$\vec{b}=\hat{j}+2 \hat{k}$,and $\vec{c}=3 \hat{i}+2 \hat{j}+\hat{k}$ are linearly dependent vectors and the magnitude of $\vec{a}$ is $\sqrt{14}$. If $\alpha$ and $\beta$ are integers,then $\alpha+\beta=$

If the volume of a parallelepiped whose coterminous edges are represented by the vectors $-12i + \alpha k$,$3j - k$,and $2i + j - 15k$ is $546$,find the value of $\alpha$.

If the vectors $a \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+b \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+c \hat{k}$ are coplanar,where $(a, b, c \neq 1)$,then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$