The Laser Interferometer Gravitational$-$Wave Observatory $($LIGO$)$ is a large$-$scale physics experiment and observatory. They use a triple hung balance to keep their laser apparatus motionless. However, they need your help. Their system got out of balance, and they need to get it back in balance. They measured and know that when they get everything balanced right, that the tension in cable $1$ will be $400$ N$,$ and the tension in cable $2$ will be $325$ N$.$ They also know that the angle between the cables will be $120.$

$($Hint: Assume this is a two dimensional problem and Pick cable $1$ to be along the positive x axis$)$

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Part $1.$ What is the sum of the forces in the X and Y directions? $($i$.$e$.$Fx$,$Fy$)$

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Part $2.$ What is the resultant force of cables $1$ and $2?$

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Part $3.$ What direction and net force is required for a $3$rd cable to offset the first two cables and satisfy the First Condition of Equilibrium?