4.1. Form the equation of the plane that is perpendicular to the vector $\vec{n}=(8,2,1)$ and passes through the point $P_{0}(3,-5,4)$.
Solution. Let's write down the coordinates of the current vector: $P_{0} M=(x-3, y+5, z-4)$. We will write the condition of orthogonality of vectors $\vec{n}$ and $\overline{P_{0} M}$ in coordinate form:

$$
\begin{aligned}
& 8(x-3)+2(y+5)+1(z-4)=0 \\
& 8 x+2 y+z-18=0
\end{aligned}
$$