So what you really need is the vector normal to that "tangent plane."
If you multiply your stress matrix by that normal vector, then that gives you the desired result (stress vector).
If you pre and post multiply by that normal vector then you have your answer to the second part of the problem (stress scalar).
The only issue is how to obtain that normal vector, and you're on your own there (google).
Draw a diagram. You will see that a radius vector from y = z = 0 at any x value is normal to the cylinder. The radius vector makes an angle of 30 degrees with the y axis, and 60 degrees with the z axis.