The foot of the perpendicular drawn from the point $(-2,-1,3)$ to a plane $\pi$ is $(1,0,-2)$. If $a, b, c$ are the intercepts made by the plane $\pi$ on $X, Y, Z$-axis respectively, then $3 a+b+5 c=$

$\mathbf{n}$ is a unit vector normal to the plane $\pi$ containing the vectors $\hat{\mathbf{i}}+3 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$. If this plane $\pi$ passes through the point $(-3,7,1)$ and $p$ is the perpendicular distance from the origin to this plane $\pi$, then $\sqrt{p^{2}+5}=$

If the harmonic conjugate of $P(2,3,4)$ with respect to the line segment joining the points $A(3,-2,2)$ and $B(6,-17,-4)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

If $L$ is the line of intersection of two planes $x+2 y+2 z=15$ and $x-y+z=4$ and the direction ratio of the line $L$ are $(a, b, c)$, then $\frac{\left(a^{2}+b^{2}+c^{2}\right)}{b^{2}}=$