Consider two cartesian coordinate system xyz and x` y` z` that initally concide. The x` y` z` undergoes three successive counterclockwise 45 rotations about the following axes: first, about the fixed z-axis;second, about its own x`-axis( which has been now rotated); finally, about its own z`-axis ( which has now been rotated);finally, about its own z`-axis (which has also been rotated). Find the components of a unit vector X in the xyz coordinate system that points along the direction of the x`-axis in rotated x` y` z` system. Attempted solution Let matrix A,B,& C denote the 3 rotation such that A denote the rotation 45 about z-axis,B rotation 45 about its x-axis,& C denote the matrix which has been rotated about its own z` axis. A = [cos 45 sin 45 0] [-sin 45 cos45 0] [0 0 1 ] B = [ 1 0 0 ] [ 0 cos45 -sin45] [ 0 sin45 cos45] C = [cos45 sin45 0] [-sin45 cos45 0] [0 0 1] I have them everything right but in my book it has in second B matrix it has j . k` as -sin45 but why is that!!?