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.

 

[jvicens]

Hi there, it seems like you are on the right track with your approach. One way to find the angle between point p and the center of the ellipsoid would be to first find the vector from the center of the ellipsoid to point p, which can be calculated by subtracting the coordinates of the center (xc, yc, zc) from the coordinates of point p (xp, yp, zp).

Next, you can calculate the unit vector of the major axis as you have done (ax/sqrt(ax^2+ay^2+az^2), ay/sqrt(ax^2+ay^2+az^2), az/sqrt(ax^2+ay^2+az^2)).

Then, you can use the dot product between the vector from the center to point p and the unit vector of the major axis to find the angle between them. The dot product can be calculated as:

cos(theta) = (v1 * v2) / (||v1|| * ||v2||)

Where v1 is the vector from the center to point p and v2 is the unit vector of the major axis. Theta represents the angle between them.

I hope this helps. Let me know if you have any further questions.