Get axis and angle of rotation of a plane

Hi all,

I have a finite plane that intersects a centreline. I know the point on the centreline of where the intersection occurs: x = 10.9, y = 13.3, z =6.4. I have attached the centreline points FYI and a plot of the plane and intersecting centreline.

My plane is defined as follows

v = [0.14 -0.28 -0.94];
x1 = 10.97;
y1 = 13.13;
z1 = 6.40;

w = null(v); % Find two orthonormal vectors which are orthogonal to v
   [P,Q] = meshgrid(-1:1); % Provide a gridwork (you choose the size)
   X = x1+w(1,1)*P+w(1,2)*Q; % Compute the corresponding cartesian coordinates
   Y = y1+w(2,1)*P+w(2,2)*Q; %   using the two vectors in w
   Z = z1+w(3,1)*P+w(3,2)*Q;

I now need MATLAB to output the axis of rotation of the plane and the angle of rotation of the plane.

Any suggestions on how to achieve this are welcome. Thanks.