1. **Problem Statement:** Define the symmetric equation of a line in 3D space and explain its components. 2. **Definition:** The symmetric equation of a line in 3D space is given by $$\frac{x - x_0}{a} = \frac{y - y_0}{b} = \frac{z - z_0}{c}$$ where $(x_0, y_0, z_0)$ is a point on the line and $(a, b, c)$ is the direction vector of the line. 3. **Explanation of Components:** - The point $(x_0, y_0, z_0)$ represents a specific location through which the line passes. - The direction vector $(a, b, c)$ indicates the direction in which the line extends in 3D space. 4. **Interpretation:** Each fraction represents how far along the line you move from the point $(x_0, y_0, z_0)$ in the direction of the vector $(a, b, c)$ to reach any point $(x, y, z)$ on the line. 5. **Summary:** The symmetric equation compactly expresses all points on the line by equating the ratios of the differences in coordinates to the components of the direction vector.