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g-M-2MB-MC-MC-MA-MA-MB-g-G-4MA-2-3MA-AB-AC-1-show-that-M-plan-g-M-g-G-4MG-2-2-Determine-the-set-of-point-M-of-plan-such-as-g-M-g-A-2-Construct-this-set-of-p




Question Number 82056 by mathocean1 last updated on 17/Feb/20
g(M)=2MB^→ .MC^→ +MC^→ .MA^→ +MA^→ .MB^→   g(G)=4MA^2 +3MA^→ (AB^→ +AC^→ )    1) show that ∀ M ∈ plan  g(M)=g(G)+4MG^2   2) Determine the set of point M of plan  such as g(M)=g(A)  2) Construct this set of point M  in the case where g(G)=5.
$${g}\left({M}\right)=\mathrm{2}{M}\overset{\rightarrow} {{B}}.{M}\overset{\rightarrow} {{C}}+{M}\overset{\rightarrow} {{C}}.{M}\overset{\rightarrow} {{A}}+{M}\overset{\rightarrow} {{A}}.{M}\overset{\rightarrow} {{B}} \\ $$$${g}\left({G}\right)=\mathrm{4}{MA}^{\mathrm{2}} +\mathrm{3}{M}\overset{\rightarrow} {{A}}\left({A}\overset{\rightarrow} {{B}}+{A}\overset{\rightarrow} {{C}}\right) \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{show}\:{that}\:\forall\:{M}\:\in\:{plan} \\ $$$${g}\left({M}\right)={g}\left({G}\right)+\mathrm{4}{MG}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{Determine}\:{the}\:{set}\:{of}\:{point}\:{M}\:{of}\:{plan} \\ $$$${such}\:{as}\:{g}\left({M}\right)={g}\left({A}\right) \\ $$$$\left.\mathrm{2}\right)\:{Construct}\:{this}\:{set}\:{of}\:{point}\:{M} \\ $$$${in}\:{the}\:{case}\:{where}\:{g}\left({G}\right)=\mathrm{5}. \\ $$

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