If $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{c}}$ are unit vectors and $\left|\overrightarrow{\mathrm{b}}\right|=4.$ If angle between $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ is ${\cos }^{-1}\left(\frac{1}{4}\right)$ and $\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}=2\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{c}},$ then $\overrightarrow{\mathrm{b}}=\mathrm{\lambda }\overrightarrow{\mathrm{a}}+2\overrightarrow{\mathrm{c}},$ where $\mathrm{\lambda }$ is equal to