Write the moment from a force about any point using both scalar and vector methods $($cross product$)$

Write the moment about a line using vectors

Identify, calculate, and use couples

Given a body with loads and moments, write an equivalent force$-$couple system as well as a single force

acting at a specific location

Three control rods attached to a lever ABC exert

the forces shown. $($a$)$ Replace the three forces

with an equivalent force$-$couple system at B$.($b$)$

Determine the single force that is equivalent to

the force$-$couple system obtained in $($a$)$ and

specify its point of application along the lever.

$(30$ points$)$