A vector ri in the XY Z frame is rotated by 30◦ about the Z axis (resulting in the xyz axes) and then translated by 12I − 2J + 7K. If the final position of the vector is rf = 5i + 9j − 6k, what is ri...

A vector ri in the XY Z frame is rotated by 30◦ about the Z axis (resulting in the xyz axes) and then translated by 12I − 2J + 7K. If the final position of the vector is rf = 5i + 9j − 6k, what is ri in terms of the XY Z coordinates?