In reply to Salma.

Your question doesn't really make sense because it is the eigenVALUES that are connected to the variance, not the eigenvectors.

Your question is really about PCA, not biplots. An eigenvalue is the variance of the data in the direction of the associate eigenvector. Eigenvectors traditionally have unit length. Also, the eigenvectors are labeled in order of the size of the eigenvalues. The first eigenvector is the direction of the greatest variance, the second eigenvector is the direction of the second greatest variance, and so on.

So, by definition, the data never have more variance in the direction of the second eigenvector. It doesn't matter what direction the eigenvectors point.