Three Dimensional Geometry: JEE Main 2023 Mathematics question

If the equation of the plane containing the line $x+2 y+3 z-4=0=2 x+y-z+5$ and perpendicular to the plane $\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2 \hat{j}+3 \hat{k})$ is $a x+b y+c z=4$, then $(a-b+c)$ is equal to :