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anonymous
 3 years ago
Find II 2e3f II assuming that e & f are unit vectors such that II e +f II=sqrt(3/2)
anonymous
 3 years ago
Find II 2e3f II assuming that e & f are unit vectors such that II e +f II=sqrt(3/2)

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0"e & f are unit vectors" meaning \(\vec{e}=1,\vec{f}=1\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0We got to sort of consider the facts here.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so e dot e=1 and f dot f also equals 1?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Okay thanks I think I know how to do it! :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I can see how \[ (\vec{e} +\vec{f}) \cdot (\vec{e} +\vec{f}) = 3/2 \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[e+f^{2}=(e+f)(e+f)=ee+2ef+ff=1+2ef+1=2+2ef=3/2\] so ef=1/4 similarly \[2e3f^{2}=(2e3f)(2e3f)=4ee12ef+9ff=1312ef=1312(1/4)=16\] therefore 2e3f=sqrt 16=4

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