Let a =3 i +2 j +2 k and b = i +2 j -2 k be two vectors. If a vector perpendicular to both the vectors a + b and a - b has the magnitude 12 then one…

Let $\displaystyle \vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k} \quad$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}-2 \hat{k}$ be two vectors. If a vector perpendicular to both the vectors $\displaystyle \overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}$ has the magnitude $\displaystyle 12$ then one such vector is :