Let P_1: r ·(2 i + j -3 k )=4 be a plane. Let P_2 be another plane which passes through the points (2, -3, 2), (2, -2, -3) and (1, -4, 2). If the…

Let $\displaystyle \mathrm{P}_1: \overrightarrow{\mathrm{r}} \cdot(2 \hat{i}+\hat{j}-3 \hat{k})=4$ be a plane. Let $\displaystyle \mathrm{P}_2$ be another plane which passes through the points ($\displaystyle 2$, -$\displaystyle 3$, $\displaystyle 2$), ($\displaystyle 2$, -$\displaystyle 2$, -$\displaystyle 3$) and ($\displaystyle 1$, -$\displaystyle 4$, $\displaystyle 2$). If the direction ratios of the line of intersection of $\displaystyle P_1$ and $\displaystyle P_2$ be $\displaystyle 16$, $\displaystyle \alpha, \beta$, then the value of $\displaystyle \alpha+\beta$ is equal to \_\_\_\_.