### Video Transcript

Two forces π
one equals 82.6 over
root three π minus π newtons and π
two equals 177.2 over root three π minus π
newtons act on an object. What force must be added to π
one
and π
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 π
three. When we consider π
three, π
one,
and π
two, weβre specifically designing π
three so that their sum is equal to
zero. That is, that the object is
subjected to a balanced force. This means that π
three is equal
to negative the sum of π
one and π
two, both of which are given in our problem
statement. If we write out π
one and π
two
as theyβre given to us and then add these two forces together, their sum is 259.8
over root three π minus π newtons. Since π
three must equal the
negative of that, π
three is negative 259.8 over root three π minus π
newtons. Thatβs the force which added to π
one and π
two will produce a net force of zero.