Find the angle and the axis of rotation for each of the 3D rotations represented by the following quaternions.
a) q₁ = √2/2 + 1/2i + 1/2k
b) q₂ = k
c) q₁ x q₂
d) q₂ x q₁
The axis of a rotation is assumed to be through the origin. A 3D rotation in quaternion form is given by Tq(p) = qpq. Show your work and give the answers in exact values.