Principal directions, ellipsoid and projection

Hello, I ha ve a symmetric 3x3 matrix (the stress), for which I have calculated it's principal directions using eig. I would like to plot the 3D ellipsoid using the eigenvectors and eigenvalues of those principal directions. Is there any function that can do that easily? Also, I would like to project that ellipsoid in the xy, xz and yz planes. If I am correct, the projection would be an ellipse, is that right? If possible, I would like to obtain both the graphical representation and the vectors defining the major and minor axes of the new ellipses. Thanks, Juan