Proof that the computed Eigen Vectors is righ?t

Hii all..

I am working in PCA to do Dimensionally Reduction. I already extract the eigen values and eigen vectors from the random distributed data (Normal Distribution data).

And I already plotted that 2 Principal Values (Eigen Vector 1 & Eigen Vector 2) along with my generated data (Normal distribution)..

My question is, how we can make sure that the eigen vectors are at right position?? I heard that we can project our data in that eigen vectors (consider that the eigen vector become the new coordinate axis) and the curve should filled the normal gaussian clue.. Which is, the center is the main and the spread of the curve is covariance..

Thankss