Why Are 1.2m and 0.45m Unnecessary for Determining Force F?

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Ry122
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In the attached diagram, if the beam was not undergoing any rotation would this be because the couple C1's forces are being canceled by the x components of the forces F and -F and also because the y components of the forces F and -F are canceling each other out?

So if C1 was known and the F force needed to be determined the values 1.2m and .45m would not be needed?
 
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No. If C1 and Fx cancel, there will be a net moment in this problem about the fixed end (try summing moments about the top left corner, and you will see that there is a net moment if C1 and Fx are equal). The only way there is no net moment is if the couple produced by F equals the negative of the couple produced by C1.