Let the equation of the plane P containing the line x+10=(8-y)/2=z be a x+b y+3 z=2(a+b) and the distance of the plane P from the point (1,27,7) be…

Let the equation of the plane $\displaystyle P$ containing the line $\displaystyle x+10=\frac{8-y}{2}=z$ be $\displaystyle a x+b y+3 z=2(a+b)$ and the distance of the plane $\displaystyle P$ from the point $\displaystyle (1,27,7)$ be $\displaystyle c$. Then $\displaystyle a^2+b^2+c^2$ is equal to $\displaystyle \_\_\_\_$.