If $m: n$ is the ratio in which the point $\left(\frac{8}{5},-\frac{1}{5}, \frac{8}{5}\right)$ divides the segment joining the points $(2, p, 2)$ and $(p,-2, p)$, where $p$ is an integer than $\frac{3 m+n}{3 n}=$

If $(\alpha, \beta \gamma)$ is the foot of the perpendicular drawn from a point $(-1,2,-1)$ to the line joining the points $(2,-1,1)$ and ( $1,1-2$ ), then $\alpha+\beta+\gamma=$

If $A(2,1,-1), B(6,-3,2), C(-3,12,4)$ are the vertices of a $\triangle A B C$ and the equation of the plane containing the $\triangle A B C$ is $53 x+b y+c z+d=0$, then $\frac{d}{b+c}=$

Let $A$ be a point having position vector $\hat{\mathbf{i}}-3 \hat{\mathbf{j}}$ and $\mathbf{r}=(\hat{\mathbf{i}}-3 \hat{\mathbf{j}})+t(\hat{\mathbf{j}}-2 \hat{\mathbf{k}})$ be a line. If $P$ is a point on this line and is at a minimum distance from the plane $\mathbf{r} .(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}})=0$, then the equation of the plane through $P$ and perpendicular to $A P$, is