# Question Video: Force Required to Balance Two Other Forces

Two forces 𝐅₁ = (82.6/√3) (𝐢 − 𝐣) N and 𝐅₂ = (177.2/√3) (𝐢 − 𝐣) N act on an object. What force must be added to 𝐅₁ and 𝐅₂ to produce a net force of zero?

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### Video Transcript

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.