Find The Angle And The Axis Of Rotation For Each Of The 3d Rotations Represented

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.

 

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