Exercise $1$:

In the coordinate system $(O,x,y,z),$ the coordinates of points A and $B$ are defined as:

$OA=\left[\begin{array}{c}3\\ 0\\ 0\end{array}\right]$;$OB=\left[\begin{array}{c}-1\\ 2\\ 1\end{array}\right]$

The moments of a wrench$/$screw at the three points $O,$A and $B$ are respectively:

$M(O)=\left[\begin{array}{c}1\\ 1\\ 4\end{array}\right]$;$M(A)=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$;$M(B)=\left[\begin{array}{c}2\\ -1\\ 9\end{array}\right]$

$1-$ Using the shifting property, determine the coordinate of the sum $S=\left[\begin{array}{c}{s}_x\\ s_y\\ s_z\end{array}\right]$

$2-$ Is it possible to reduce the wrench$/$screw to a unique sliding vector?

$3-$ Determine the central axis of the wrench$/$screw$.$ Draw it$.$

$4-$ Find the value of the moment on the central axis

$5-$ Deduce the minimum moment amplitude

$6-$ Prove that the moments at points $O,$A and $B$ are actually moments of a wrench...