$7.30$ points

For the force vectors vec$(F{)}_1=F_{1,x}$hat$()+F_{1,y}$hat$()+F_{1,z}$hat$(k)$ and vec$(F{)}_2=F_{2,x}$hat$()+F_{2,y}$hat$()+F_{2,z}$hat$(k)$ located at vec$(r{)}_1=x_1$hat$()+z_1$hat$(k)$ and vec$(r{)}_2=y_2$hat$()+z_2$hat$(k),$ respectively. What are the resultant and couple of these two vectors?

Write down the general formulas for the resultant and couple of a system of vectors

Calculate the resultant of the system of forces

Calculate the moment of each of the forces

Calculate the couple of the system of forces

Show by dimensional analysis that vec$(C)$ has dimensions of moment

Insert values vec$(F{)}_1=(5$hat$()+4$hat$()+3$hat$(k))N,$vec$(F{)}_2=(-2$hat$()+-1$hat$()+2$hat$(k))N,$vec$(r{)}_1=(2$hat$()-2$hat$(k))m$ and vec$(r{)}_2=(hat()+$hat$(k))m$ to find the values of vec$(R)$ and vec$(C)$

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