Video Transcript
Given that ๐น one, ๐น two, and ๐น three are three coplanar forces in equilibrium meeting at a point where ๐น one equals five ๐ minus three ๐ and ๐น two equals four ๐ minus 14๐, find ๐น three.
As the three forces are in equilibrium, ๐น one plus ๐น two plus ๐น three must be equal to zero ๐ plus zero ๐. Substituting in the values of force, ๐น one and ๐น two, gives us five ๐ minus three ๐ plus four ๐ minus 14๐ plus ๐น three equals zero ๐ plus zero ๐.
Grouping the like terms on the left-hand side gives us nine ๐ minus 17๐ plus ๐น three is equal to zero ๐ plus zero ๐, as five ๐ plus four ๐ is equal to nine ๐ and negative three ๐ minus 14๐ is negative 17๐.
Balancing this equation by subtracting nine ๐ and adding 17๐ to both sides of the equation gives us ๐น three is equal to negative nine ๐ plus 17๐. This means that, in order for the three coplanar forces to be in equilibrium, where ๐น one equals five ๐ minus three ๐ and ๐น two equals four ๐ minus 14๐, then ๐น three must be equal to negative nine ๐ plus 17๐.