Find symmetric equations of the line that contains the point $(5,-2, 3)$ and is in the direction of the vector $\mathbf{D=}$ $3\mathbf{i}-2\mathbf{k}$.

Solution For $\mathbf{D=}$ $3\mathbf{i}-2\mathbf{k}$, $a=3$, $b=0$, and $c=-2.$ So, symmetric equations in the direction $\mathbf{D}$ are $$\dfrac{x-5}{3}=\frac{z-3}{-2}\qquad y=-2$$