If a and b are two vectors such that a = i - j + k and b =2 i - j -3 k, then find the vector c, given that a × c = b and a · c =4.

If $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}$ are two vectors such that $\displaystyle \overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-3 \hat{\mathrm{k}}$, then find the vector $\displaystyle \overrightarrow{\mathrm{c}}$, given that $\displaystyle \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=4$.