Compute the matrix which corresponds with the transformation

Compute the matrix which corresponds with the transformation in R^3 which consists in first rotating counter-clockwise about the vertical z-axis through the angle pi/3 and then about the y-axis counterclockwise through angle pi/4. Consult the lecture slides for the required rotation matrices if necessary. Verify that the matrix you obtain is orthogonal.

Solution

Code in malab for calculating thr required transformations:

Rz=[cos(60) sin(60) 0 0 ; -sin(60) cos(60) 0 0 ;0 0 1 0;0 0 0 1];
Ry=[cos(45) 0 -sin(45) 0 ; 0 1 0 0 ;sin(45) 0 cos(45) 0;0 0 0 1];

T= Rz*Ry

Ans: Transformation about z axis and y is given by

T =

-0.5003 -0.3048 0.8104 0
0.1601 -0.9524 -0.2594 0
0.8509 0 0.5253 0
0 0 0 1.0000