Let p =2 i +3 j + k and q = i +2 j + k be two vectors. If a vector r =(α i +β j +γ k ) is perpendicular to each of the vectors ( p + q ) and ( p - q…

Let $\displaystyle \overrightarrow{\mathrm{p}}=2 \hat{i}+3 \hat{j}+\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{q}}=\hat{i}+2 \hat{j}+\hat{k}$ be two vectors. If a vector $\displaystyle \overrightarrow{\mathrm{r}}=(\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k})$ is perpendicular to each of the vectors $\displaystyle (\overrightarrow{\mathrm{p}}+\overrightarrow{\mathrm{q}})$ and $\displaystyle (\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{q}})$, and $\displaystyle |\overrightarrow{\mathrm{r}}|=\sqrt{3}$, then $\displaystyle |\alpha|+|\beta|+|\gamma|$ is equal to \_\_\_\_.