I am currently learning about creating the vector equation for a line parametrically from using the Point-Direction form of a line. (If that makes sense, please correct my understanding/wording). I understand how to find the vector equation of a line given 2 points.
(Ex. https://www.quora.com/How-do-you-find-the-vector-equation-of-a-line-when-given-two-points).
But I am confused as to how this question works as it deals with a plane instead of a line.
Use vector notation to describe the points that lie in the given configuration. (Let s and t be elements of the Reals.)
the plane spanned by
**v**1 = (8, 4, 0)
and
**v**2 = (0, 8, 4)
Answer: **l**(s,t) = (8s, 4s + 8t, 4t)
The plane in $R^3$ that's equivalent to span$(v_1,v_2)$ is $$\left\{x|x = sv_1 + tv_2 = s\left( \begin{array}{c} 8 \\ 4\\ 0 \end{array}\right) + t \left( \begin{array}{c} 0 \\ 8\\ 4 \end{array}\right) = \left( \begin{array}{c} 8s \\ 4s+8t\\ 4t \end{array}\right)\right\}.$$