Okay so I am struggling to understand this.
For a rectangular 3D object in $R^3$
My book states: ..shows a rigid body with frame x-y-z attached to it. Our representation of the orientation of the body will be the 3x3 matrix:
$R = \\ x_.1,y_.1,z_.1\\ x_.2,y_.2,z_.2\\ x_.3,y_.3,z_.3;$
Where $x = [x_.1 x_.2 x_.3]^T$ is the unit vector in the body x direction expressed in the stationary coordinate frame $x_.s,y_.s,z_.s$
The vectors y and z are defined similarly.
I think I understand why the columns are unit vectors - but I do not understand what the intuition is behind the rows being unit vectors? Would greatly appreciate some help.
Since $R^TR=I$, we also have $RR^T=I$, so the rows dotted with themselves and each other are also $1$ and $0$.