By definition, the three principal stresses ($\sigma_1 \geq \sigma_2 \geq \sigma_3$) act mutually perpendicular to each other. The intermediate principal stress $\sigma_2$ acts parallel to the plane containing $\sigma_1$ (maximum) and $\sigma_3$ (minimum). This is fundamental in Mohr circle construction: $\sigma_2$ plots as a point on the $\sigma$-axis and does not define a failure envelope in 2D analysis.