Question $3)(20$ points$)$ Using the coordinates of three markers in the global coordinate system affixed to the socket,

you create a local socket coordinate system consisting of three, orthogonal unit vectors. The origin of the socket

coordinate system defined in terms of the global coordinate system is located at $0\mathrm{.}2m,0\mathrm{.}65m$ and $-0\mathrm{.}08$ m in the $x,y$

and $z$ directions, respectively.

The unit vectors that you computed defining $x,Y,$ and $Z$ axes of the socket coordinate system with respect to the

global coordinate system are as follows:

vec$(x)=0\mathrm{.}6086{}^{}-0\mathrm{.}4082{}^{}+0\mathrm{.}4530k^{}$

vec$(Y)=-0\mathrm{.}557{}^{}+0\mathrm{.}2652{}^{}+-1\mathrm{.}86{10}^{-5}$vec$(k)$

vec$(Z)=0\mathrm{.}2676{}^{}-05345{}^{}-0\mathrm{.}222k^{}$

The point of intersection of the pylon and the socket shown at point $P$ is important to track. If the coordinates of

point $P$ defined in the socket coordinate system are: $(x=0\mathrm{.}03m,y=0\mathrm{.}06m,z=0\mathrm{.}01m),$ what are the coordinates of

point $P$ in the global coordinate system?