Let a = i + j - k and c =2 i -3 j +2 k. Then the number of vectors b such that b × c = a and | b | ∈{1,2, ….., 10} is:

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