Calculate the angle between plane normal and a point it cuts

I am trying to write a script that will calculate the angle between two 3D vectors. Specifically I have a plane cutting through a model where the centre of the plane cuts a point along the centreline of the model as shown in the attached image. One 3D vector is the plane normal e.g [0.21 0.98 0], the other 3D vector is the position of the point it cuts e.g [4.05 5.35 3.96]. By having this angle I will be able to adjust the plane to be perpendicular to the inlet of the model!

Any suggestions on how to achieve this are welcome!

Thanks

[James Tursa]

How can you determine the angle of the plane to the inlet by just knowing the centerline point of the inlet that it intersects? Seems like you need another point or something to give the direction of the inlet. Then you can find the angle between these vectors.

Answer 1

[Fabio Freschi]

using the definition of dot product:

% angle function in radians
ang = @(u,v)acos(dot(u,v)/(norm(u)*norm(v)));

% data
u = [0.21 0.98 0];
v = [4.05 5.35 3.96];

% calculation
myangle = ang(u,v)