In Maple:

1. Verify that formula (7.74) in PRO-2012-Lecture-12.pdf for quaternion composition holds true.
2. Verify that formula (7.76) in PRO-2012-Lecture-12.pdf for quaternion composition holds true.
   1. Find the quaternion representation r1 and matrix representation R1 of the rotation by Pi/2 around x-axis.
   2. Find the quaternion representations quaternion representation r2 and matrix representation R2 of the rotation by Pi/2 around y-axis.
   3. Construct the quaternion representations r21 of the rotation r21 = r2 o r1 using the composition 'o' of quaternions.
   4. Find the rotation matrix R21 = R2.R1 by matrix multiplication '.'.
   5. Construct the rotation matrix from r21 and compare it to R21.
   6. Construct the quaternion from the rotation matrix R21 and compare it to r21. (Hint: R→axis & angle→quaternion).

Upload via the course ware the zip archive hw06.zip containing

1. hw06.mws Maple script (functions) solving the assignment.
2. hw06.pdf description of the solution (algorithms, results, comments).