Solution:

Vector is a palm-sized robot that uses the same general design as Cozmo, Anki's previous robot toy.

Vector is made from a black plastic material and he has a body that's filled with various sensors and electronics to detect and respond to the environment around him.

In rectangular coordinates the orientation of the tool is expressed by a Rotation matrix $R$ $={\mathrm{r} 1, \mathrm{r} 2, \mathrm{r} 3}$ 3 columns of $\mathrm{R}$ coordinates correspond to the normal, sliding and approach as shown in the above diagram. $\mathrm{r} 3=$ approach vector i.e. it is aligned along with the Tool Roll axis and always point away from the wrist. r2= sliding vector i.e. orthogonal to the approach vector, align to the opening and closing of the gripper. $\mathrm{rl}=$ normal vector i.e. orthogonal to the plane defined by the $\mathrm{r} 3$ and $\mathrm{r} 2$ and to complete Right -handed Orthonormal coordinate frame.