4.7. Form the equation of the line passing through the given point $P_{0}(3,4,2)$ and perpendicular to the plane $8 x-4 y+5 z-4=0$
Solution. Let's find the coordinates of the current vector of the desired line $\widehat{P}_{0} M=(x-3, y-4, z-5)$. Since the line is perpendicular to the plane, the direction vector of the line is the normal vector of the plane $\vec{n}=(8,4,5)$. We write the condition of collinearity of vectors $\overrightarrow{P_{0} M}$ and $\vec{n}$, and obtain the equation of the line:

$$
(x-3) / 8=(y-4) /(-4)=(z-2) / 5
$$