I am trying to visualize the following rotation of R^3, but it is very difficult. I want to get the answer by intuition, and not by using the Rodrigues rotation formula or conjugation of matrices, etc.
Problem statement: Determine the matrix that represents the following rotation of R^3: an angle of pi/2 about the fixed axis containing the vector (1,1,0)^t
Here is what I have tried in my diagram:
Should I find a 3x3 rotation matrix A such that A(1,1,0)^t=(-1,1,0)^t?