If vectors $\overrightarrow{\mathrm{a}}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}-\widehat{\mathrm{k}},\overrightarrow{\mathrm{b}}=2\widehat{\mathrm{i}}-\widehat{\mathrm{j}}+\widehat{\mathrm{k}}\text{ and }\overrightarrow{\mathrm{c}}=\mathrm{\lambda }\widehat{\mathrm{i}}+\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}$are coplanar, hen find the value of $\left(\mathrm{\lambda }-4\right)$

Vector $\overrightarrow{\mathrm{a}}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}-\widehat{\mathrm{k}},\overrightarrow{\mathrm{b}}=2\widehat{\mathrm{i}}-\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$ ,$\overrightarrow{\mathrm{c}}=\mathrm{\lambda }\widehat{\mathrm{i}}+\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}$ are coplanar

$\begin{array}{l}\Rightarrow \left|\begin{array}{ccc}1& 2& -1\\ 2& -1& 1\\ \lambda & 1& 2\end{array}\right|=0\\ \text{ or }\lambda -3+2(-5)=0\\ \text{ or }\lambda =13\end{array}$