Discover Linear Algebra: A first course in linear algebra

the vector equation \(\uvec{x} = \uvec{x}_0 + t \uvec{p}\text{,}\) where \(\uvec{x}_0\) is a vector from the origin to a known point on the line, \(\uvec{p}\) is a known parallel vector for the line, \(\uvec{x}\) 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 \(\uvec{x}\) varies

the vector equation \(\uvec{x} = \uvec{x}_0 + s \uvec{p}_1 + t \uvec{p}_2\text{,}\) where \(\uvec{x}_0\) is a vector from the origin to a known point on the plane, \(\uvec{p}_1,\uvec{p}_2\) are known parallel vectors for the plane that are not parallel to each other, \(\uvec{x}\) 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 \(\uvec{x}\) varies