Elasticity: Determine zero normal stress plane

[Zipi Damn]

Given the stress tensor in a point, determine the zero normal stress plane.
...2 3 0
T= 3 2 0
...0 0 5
----------------------
Eigenvalues: σ1=σ2=5, σ3=-1
It must be simple, but I don't know how to determine the normal vector of that plane analytically.

I know σ=0.
t=Tn=σ+τ=τ
If normal stress σ equals zero, ¿the shear stress will be the maximum value of τ ((σ1-σ3)/2)?

Taking a look to Mohr's circle I think τ in that plane must be the intersection between the circunference and the τ axis, but that's not τmax.

I'm confused.

 

[Zipi Damn]

Okay, I think I got it.

Using the equation of the mayor circunference of center (0,2) and radius R=3 from Mohr's circle, we make σ=0. Then we isolate the shear stress.

(σ-2)²+(τ-0)²=3²

τ=√5

Now that I have the modulus, I want to know the normal direction of the plane in which shear stress equals √5.