88. Form the equation of the line passing through the point $A(3, -2)$ and having the direction vector $\vec{n}=(-5, 3)$.
Solution. $1^{0}$. Choose a point $M(x ; y) \in l$.

$2^{0}$. Find the vector $\overrightarrow{A M}=(x-3 ; y+2)$.

$3^{0}$. Direction vector $\vec{n}=(-5 ; 3)$.

$4^{\circ}$. Write the equation of the line:

$$
\frac{x-3}{-5}=\frac{y+2}{3}
$$

from which $3 x-9=-5 y-10 ; 3 x+5 y+1=0$ - the desired equation in general form.