If a =2 i + y j + k and b = i +2 j +3 k are two vectors for which the vector ( a + b ) is perpendicular to the vector ( a - b ), then find all the…

If $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\mathrm{y} \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ are two vectors for which the vector $\displaystyle (\vec{\mathrm{a}}+\vec{\mathrm{b}})$ is perpendicular to the vector $\displaystyle (\vec{\mathrm{a}}-\vec{\mathrm{b}})$, then find all the possible values of y.