Let $\overrightarrow{a} = \hat{i} + \hat{j} + \hat{k}, \overrightarrow{b} = \hat{i} - \hat{j} + 2 \hat{k}$ and $\overrightarrow{c} = x \hat{i} + ( x - 2)\hat{j} - \hat{k}$. If the vector $\overrightarrow{c}$ lies in the plane of $\overrightarrow{a}$ and $\overrightarrow{b}$, then $x$ equals :

Question

( A ) $-2$
( B ) $0$
( C ) $-4$
( D ) $1$