Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. Then the number of vectors $\overrightarrow{\mathrm{b}}$ such that $\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}$ and $|\overrightarrow{\mathrm{b}}| \in\{1,2, \ldots \ldots, 10\}$ is