Using the standard basis (î ĵ k̂) for vectors in three dimensions:
(a) Construct the matrix representing a rotation through angle θ (counterclockwise, looking down the axis toward the origin) about the z axis.
(b) Construct the matrix representing a rotation by 120 (counterclockwise, looking down the axis) about an axis through the point (1,1,1).
(c) Construct the matrix representing reflection through the xy plane.
(d) Check that all these matrices are orthogonal, and calculate their determinants.