find the coordinates of the point on the ellipsoid where the major axis meet

ppmko

I have a point p(xp,yp,zp) inside an ellipsoid and i want to find the angle of that point from the center of the ellipsoid(xc,yc,zc) .

I also have
the major axis length 'a' ,with length ax,ay and az components

I calculated the unit vector of axis a with formula length of axis 'a"/sqrt(ax^2+ay^2+az^2).

how do i find the angle at which p makes with the center of ellipsoid from the from axis a



I calculated the coordinates of the point that intersect the major axis on the ellipsoid using the unit vector by calculating the xcoordinate as ax/sqrt(ax^2+ay^2+az^2) similarly for y and z coordinates
this give me 2 set of coordinates .now i have new coordinates of the point that intersects the major axis on the ellipsoid and the coordinates of p . Now i use distance formula and then use the cosine law for triangles to find the angle betwen the point p and the center of the ellipsoid.pls let me know if this is correct.