ECE 417 --- ROBOTICS
Homework 1, Spring 2021

 For the rotation matrix:
 

XYZRUVW =	[	2/7	-6/7	3/7	]
		6/7	3/7	2/7
		-3/7	2/7	6/7

1. Show that ^XYZR_UVW  is a proper rotation matrix.

2. Show that R^-1 is equal to R^T where (R is shorthand for ^XYZR_UVW).  HINT: taking the inverse is not required.

3. Compute R A where matrix A is given by

A   =	[	3/7	2/7	6/7	]
		2/7	6/7	-3/7
		-6/7	3/7	2/7

4. If P_UVW = (1,2,3)^T, what is P_XYZ given (using ^XYZR_UVW above)

5. If P_XYZ = (1,2,3)^T, what is P_UVW? given (using ^XYZR_UVW above)

6. If the OUVW system has basis vectors U = (1/√2, 0, 1/√2)^T, V = (-1/√2, 0, 1/√2)^T, W = (0, -1, 0)^T, and the OXYZ system has basis vectors X = (1, 0, 0)^T, Y = (0, 1/√2, -1/√2)^T, Z = (0, 1/√2, 1/√2)^T, then what is the corresponding rotation matrix between the two systems?