In the figure particles $2$ and $4,$ of charge $-e,$ are fixed in place on a $y$ axis, at $y_2=-11\mathrm{.}9cm$ and $y_4=5\mathrm{.}95cm.$ Particles $1$ and $3,$ of charge $e,$ can be moved along the $x$ axis. Particle $5,$ of charge $+e,$ is fixed at the origin. Initially particle $1$ is at $x_1=-11\mathrm{.}9cm$ and particle $3$ is at $x_3=11\mathrm{.}9cm.($a$)$ To what $x$ value must particle $1$ be moved to rotate the direction of the net electric force vec$(F{)}_{\text{n}\text{e}\text{t}}$ on particle $5$ by $30$ counterclockwise? $($b$)$ With particle $1$ fixed at its new position, to what $x$ value must you move particle $3$ to rotate back to its original direction?

$($a$)$ Number

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$($b$)$ Number

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