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minyayao
Group Title
Find II 2e3f II assuming that e & f are unit vectors such that II e +f II=sqrt(3/2)
 one year ago
 one year ago
minyayao Group Title
Find II 2e3f II assuming that e & f are unit vectors such that II e +f II=sqrt(3/2)
 one year ago
 one year ago

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wio Group TitleBest ResponseYou've already chosen the best response.2
"e & f are unit vectors" meaning \(\vec{e}=1,\vec{f}=1\)
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.2
We got to sort of consider the facts here.
 one year ago

minyayao Group TitleBest ResponseYou've already chosen the best response.2
so e dot e=1 and f dot f also equals 1?
 one year ago

minyayao Group TitleBest ResponseYou've already chosen the best response.2
Okay thanks I think I know how to do it! :)
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.2
I can see how \[ (\vec{e} +\vec{f}) \cdot (\vec{e} +\vec{f}) = 3/2 \]
 one year ago

minyayao Group TitleBest ResponseYou've already chosen the best response.2
\[e+f^{2}=(e+f)(e+f)=ee+2ef+ff=1+2ef+1=2+2ef=3/2\] so ef=1/4 similarly \[2e3f^{2}=(2e3f)(2e3f)=4ee12ef+9ff=1312ef=1312(1/4)=16\] therefore 2e3f=sqrt 16=4
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.2
Wonderful thinking.
 one year ago

oldrin.bataku Group TitleBest ResponseYou've already chosen the best response.0
$$e_x^2+e_y^2=1\\f_x^2+f_y^2=1\\(e_x+f_x)^2+(e_y+f_y)^2=\frac32\\e_x^2+2e_xf_x+f_x^2+e_y^2+2e_yf_y+f_y^2=\frac32\\2+2e_xf_x+2e_yf_y=\frac32\\e_xf_x+e_yf_y=\frac14\\(2e_x3f_x)^2+(2e_y3f_y)^2=4e_x^212e_xf_x+9f_x^2+4e_y^212e_yf_y+9f_y^2\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =4+912[e_xf_x+e_yf_y]\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =13+3=16\\\Vert 2e3f\Vert=\sqrt{16}=4$$
 one year ago

minyayao Group TitleBest ResponseYou've already chosen the best response.2
Thank you!
 one year ago
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