1. The problem statement, all variables and given/known data 3.) Stress analysis at a critical point in a machine member gives the three-dimensional state of stress in MPa as the following: y = [ 105 0 0 0 -140 210 0 210 350 ] Using the eigenvalue formulation to find the principal stresses (eigenvalues) and principal directions (eigenvectors). Show these stresses on a properly oriented element. Use the three-dimensional Mohr’s circle to obtain the maximum shear stress and show this on a properly oriented element. Repeat this problem using MATLAB. 2. Relevant equations I can do all except finding the directions. I'm not sure how to find that. Do i just plug back my eigenvalues into mhy homogeneous eqn? 3. The attempt at a solution skipping some steps: det( 105 - s 0 0 0 -140 - s 210 =  0 210 350 - s ) Solving for S (using characteristic eqn): S = 105, 427.68, -217.68 These are my eigenvalues. In a previous step, my homogeneous eqn was: [ 105 - s 0 0 0 -140 - s 210 * [l;m;n] =  0 210 350 - s ] If i plug my S values back in, i dont know how to solve.