Has this Principal Component Analysis (PCA) been done correctly? I have a set of 3D data points, indicated by the blue color in the picture below.

I then project them onto the x-y plane, i.e. setting z values of all the points to 0, shown by the yellow color below.

Then, I perform PCA on the 2D data points (the yellow ones).

I end up with the 1st Principal Component being the green line, and the 2nd being the yellow line.



As I am a newbie in PCA, I am not sure whether I have done something wrong or not.

Because in my intuitive, the 1st Principal Component should be like in the picture below:



I mean unlike the above picture given in wiki, my 1st component is NOT obvious and seems to make no sense. Did I do something wrong?

Edit:

To avoid the confusion, the 2D view from the above is as follows:
If the PCA was correct, than green and yellow line would be perpendicular. So something is wrong with your result.