Stress vector that acts on the plane

Question

A flat plate with dimensions 110x220 mm is subject to the indicated stresses.
Assume that $sigma_{zz} = 120 MPa$.
Determine the stress vector that acts on the plane defined by the z axis and the dashed line segment.
In the solution it is written that
$$theta = 90^o - arctanleft(frac{0.11}{0.22}right)$$
$$n(theta= 63.43^o) = [costheta, sintheta, 0 ] = [0.44730,   0.89440,   0]$$
I thought that θ=0 and therefore n=[0 0 1] since so n is perpendicular to the plane.
Why I am wrong?
Could someone explain me?

NMech · Answer

$vec{n}$ is the normal of the plane which is defined by z (red) , and the dashed line (green).

The direction of the green line can be obtained by the diagonal (apologies for the bad drawing). $theta$ is denoted with blue.
From the right angle you can see that:
$$tantheta = frac{110}{220} Rightarrow$$
$$theta = arctanleft(frac{110}{220}right) $$
Essentially it has the same direction as y' in the figure you are showing.
However, I would have expected the vector to be
$$vec{n}= [-sintheta, costheta, 0]$$
Are you sure, you've written the correct formula?

Stress vector that acts on the plane

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