Let a =2 i -3 j + k, b =3 i +2 j +5 k and a vector c be such that ( a - c ) × b =-18 i -3 j +12 k and a · c =3. If b × c = d, then | a · d | is equal…

Let $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}-3 \hat{j}+\hat{k}, \quad \overrightarrow{\mathrm{~b}}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\displaystyle \overrightarrow{\mathrm{c}}$ be such that $\displaystyle (\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{c}}) \times \overrightarrow{\mathrm{b}}=-18 \hat{i}-3 \hat{j}+12 \hat{k}$ and $\displaystyle \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=3$. If $\displaystyle \overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{d}}$, then $\displaystyle |\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{d}}|$ is equal to: