A vector tangent to r(t) is dr/dt. Evaluate at t = 1 and you have the normal vector to the plane.

r(1) gives the position vector of a point in the plane.

So you have a normal to the plane and a point in the plane.

The equation of a plane is ax + by + cz = d where <a, b, c> is a normal to the plane and d is found by substituting a known point into ax + by + cz = d (once you've substituted the values of a, b and c of course).