Let u be a vector coplanar with the vectors a =2 i +3 j - k and b = j + k. If u is perpendicular to a and u · b =24, then | u |^2 is equal to:

Let $\displaystyle \overrightarrow{\mathrm{u}}$ be a vector coplanar with the vectors $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{j}+\hat{k}$. If $\displaystyle \overrightarrow{\mathrm{u}}$ is perpendicular to $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{u}} \cdot \overrightarrow{\mathrm{b}}=24$, then $\displaystyle |\overrightarrow{\mathrm{u}}|^2$ is equal to :