Hand written solution required

The IJK system needs to be transformed into a new coordinate system LMN in order to better control the maneuver of a satellite. This coordinate transformation requires three rotations, in the following order: i. 30" about the I axis; ii. 45\" about the K axis; iii. 70\" about the J axis. (a) Find the required transformation matrix. (b) Transform the vector r = 2 I 0.5 J + 3 K to the LMN system. (c) Transform the vector 1' = 0.2 L 0.4 M + 0.1 N to the IJK system