A plane is determined by three points or by two direction vectors and a point, now you've given one direction vector and two points, so you need to find another direction vector.
EDIT:
Do you want a vector equation or a cartesian equation?
A plane is determined by three points or by two direction vectors and a point, now you've given one direction vector and two points, so you need to find another direction vector.
EDIT:
Do you want a vector equation or a cartesian equation?
This is the way I would do it:
Given a plane and two points and the plane is parallel to a line who's direction ratios are . In general the vector equation of a plane through one point and with two directions vectors is: . Now we already have (we work now in a three dimensional space): . Can you determine the other direction vector ?
.