Problem
The structure \( A B C D E \) consisting of the straight, rigid rods with length \( a, b \) and \( c \) connected perpendicularly to each other is loaded with the force system seen in the figure consisting of concentrated forces and couples. The sense of vectors \( \mathbf{F}_{2}, \mathbf{F}_{3} \) and \( \mathbf{M}_{2} \) is according to the figure, their line of action is parallel to one of the coordinate axes. The orientation of vectors \( \mathbf{F}_{1} \) and \( \mathbf{M}_{1} \) is according to the given data.
1. Make a scaled axonometric figure of the excercise based on the given data!
2. Determine the reduced vector couple \( \left(\left[\mathbf{F}, \mathbf{M}_{O}\right]_{O}\right) \) of the given force system reduced into the origo!
3. Calculate the moment \( M_{f} \) of the force system onto the axis \( f \) with direction same as the line of action of force \( \mathbf{F} \) !
4. Find the closest point \( G\left(x_{G}, y_{G}, z_{G}\right) \) of the central line \( e \) to the origo and determine the reduced vector couple \( \left(\left[\mathbf{F}, \mathbf{M}_{G}\right]_{G}\right) \) to that point \( G \) ! Chech Your result with the moment \( M_{f} \) calculated in the previous step!
5. Draw Your results into the figure!
Data
(indecees \( x, y \) and \( z \) stand for the given coordinates, while the direction of vectors \( \mathbf{F}_{2}, \mathbf{F}_{3} \) and \( \mathbf{M}_{2} \) is according to the figure)
\begin{tabular}{|c|c|c||ccc|c|c||ccc|c|}
\hline \begin{tabular}{c}
\( a \) \\
{\( [\mathrm{~m}] \)}
\end{tabular} & \begin{tabular}{c}
\( b \) \\
{\( [\mathrm{~m}] \)}
\end{tabular} & \begin{tabular}{c}
\( c \) \\
{\( [\mathrm{~m}] \)}
\end{tabular} & \begin{tabular}{c}
\( F_{1 x} \) \\
{\( [\mathrm{kN}] \)}
\end{tabular} & \begin{tabular}{c}
\( F_{1 y} \) \\
{\( [\mathrm{kN}] \)}
\end{tabular} & \begin{tabular}{c}
\( F_{1 z} \) \\
{\( [\mathrm{kN}] \)}
\end{tabular} & \begin{tabular}{c}
\( F_{2} \) \\
{\( [\mathrm{kN}] \)}
\end{tabular} & \begin{tabular}{c}
\( F_{3} \) \\
{\( [\mathrm{kN}] \)}
\end{tabular} & \begin{tabular}{c}
\( M_{1 x} \) \\
{\( [\mathrm{kNm}] \)}
\end{tabular} & \begin{tabular}{c}
\( M_{1 y} \) \\
{\( [\mathrm{kNm}] \)}
\end{tabular} & \begin{tabular}{c}
\( M_{1 z} \) \\
{\( [\mathrm{kNm}] \)}
\end{tabular} & \begin{tabular}{c}
\( M_{2} \) \\
{\( [\mathrm{kNm}] \)}
\end{tabular} \\
\hline 0.4 & 0.3 & 0.4 & 3 & -1 & -1 & 1 & 1.3 & 0.5 & 0.5 & 0.3 & 1.4 \\
\hline
\end{tabular}
(Partial) results