Two forces 𝐅 one equals 82.6 over
root three 𝑖 minus 𝑗 newtons and 𝐅 two equals 177.2 over root three 𝑖 minus 𝑗
newtons act on an object. What force must be added to 𝐅 one
and 𝐅 two to produce a net force of zero?
We can name the force that we want
to solve for to make all the forces add up to zero together 𝐅 three. When we consider 𝐅 three, 𝐅 one,
and 𝐅 two, we’re specifically designing 𝐅 three so that their sum is equal to
zero. That is, that the object is
subjected to a balanced force. This means that 𝐅 three is equal
to negative the sum of 𝐅 one and 𝐅 two, both of which are given in our problem
statement. If we write out 𝐅 one and 𝐅 two
as they’re given to us and then add these two forces together, their sum is 259.8
over root three 𝑖 minus 𝑗 newtons. Since 𝐅 three must equal the
negative of that, 𝐅 three is negative 259.8 over root three 𝑖 minus 𝑗
newtons. That’s the force which added to 𝐅
one and 𝐅 two will produce a net force of zero.