1. The problem is to determine if two lines $a$ and $b$ are coplanar, meaning they lie in the same plane. 2. Two lines are coplanar if they are either parallel, intersecting, or if the shortest distance between them is zero. 3. The formula to check if two lines are coplanar involves the scalar triple product of their direction vectors and the vector connecting points on each line: $$\text{Lines } a \text{ and } b \text{ are coplanar if } (\vec{d_a} \times \vec{d_b}) \cdot \vec{P_aP_b} = 0$$ where $\vec{d_a}$ and $\vec{d_b}$ are direction vectors of lines $a$ and $b$, and $\vec{P_aP_b}$ is the vector between points on each line. 4. If the scalar triple product equals zero, the lines are coplanar; otherwise, they are skew (non-coplanar). 5. To apply this, find direction vectors and a vector between points on each line, compute the cross product, then the dot product. 6. If you provide coordinates or parametric equations of lines $a$ and $b$, I can compute this explicitly.