Finding Symmetric Equations of a Line

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 \[ \dfrac{x-5}{3}=\frac{z-3}{-2}\qquad y=-2 \]