The plane equation is given as:
$\vec r = \vec r_0 + \lambda \vec a + \mu \vec b$
I understand that we can express line as a vector (although I'm not totally clear on that concept either), but what I really don't understand is how can a vector represent a plane?
I understand that we can represent any point on the plane by choosing the right $\lambda$ and $\mu$ (then we "walk around the plane), but what does $\vec r_0$ have to do with any of this? And again, how can a vector respresent an entire plane?
Thanks in advance!
A line can be described by
$$\vec r = \vec r_0 + \lambda \vec a$$ and you get all the points (an infinity of them) along the line by varying $\lambda$. In particular, with $\lambda=0$ you see that the line is through $\vec r_0$. The line is parallel to $\vec a$.
Similarly a plane can be described by
$$\vec r = \vec r_0 + \lambda \vec a+ \mu \vec b$$ and you get all the points (a double infinity of them) on the plane by varying $\lambda$ and $\mu$. In particular, with $\lambda=\mu=0$ you see that the plane is through $\vec r_0$. The plane is parallel to both vectors $\vec a,\vec b$.