vector problem

Nov 2019
1
0
New York
Hi all,

Please take a look at the attached image of the problem and if someone could explain where the indicated value came from that would be so very helpful. I got everything but not quite sure why the sqrt2 was inserted towards the end.
 

Attachments

Jun 2016
13
15
UK
Hi all,

Please take a look at the attached image of the problem and if someone could explain where the indicated value came from that would be so very helpful. I got everything but not quite sure why the sqrt2 was inserted towards the end.
It's because $F_{4x} = F_{4y}$ which means that

$F_4 = \sqrt{ F^2_{4x} + F^2_{4y} } = \sqrt{ F^2_{4x} + F^2_{4x}} = \sqrt{2F^2_{4x} } = \sqrt{2}|F_{4x}|$

hence the $\sqrt{2}$ as a factor.
 
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