Discover Linear Algebra: A first course in linear algebra

the vector equation $\mathbf{x}={\mathbf{x}}_0+t\mathbf{p}\text{,}$ where ${\mathbf{x}}_0$ is a vector from the origin to a known point on the line, $\mathbf{p}$ is a known parallel vector for the line, $\mathbf{x}$ is a variable vector representing an arbitrary point on the line (again as a vector from the origin), and $t$ is a scalar parameter that varies as the arbitrary vector $\mathbf{x}$ varies

the vector equation $\mathbf{x}={\mathbf{x}}_0+s{\mathbf{p}}_1+t{\mathbf{p}}_2\text{,}$ where ${\mathbf{x}}_0$ is a vector from the origin to a known point on the plane, ${\mathbf{p}}_1,{\mathbf{p}}_2$ are known parallel vectors for the plane that are not parallel to each other, $\mathbf{x}$ is a variable vector representing an arbitrary point on the plane (again as a vector from the origin), and $s,t$ are scalar parameters that vary as the arbitrary vector $\mathbf{x}$ varies