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.


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Question Number 82056 by mathocean1 last updated on 17/Feb/20

$g (M) = 2 M \vec{B} . M \vec{C} + M \vec{C} . M \vec{A} + M \vec{A} . M \vec{B}$ $g (G) = 4 {M A}^{2} + 3 M \vec{A} (A \vec{B} + A \vec{C})$ $1) s h o w t h a t \forall M \in p l a n$ $g (M) = g (G) + 4 {M G}^{2}$ $2) D e t e r m i n e t h e s e t o f p o i n t M o f p l a n$ $s u c h a s g (M) = g (A)$ $2) C o n s t r u c t t h i s s e t o f p o i n t M$ $i n t h e c a s e w h e r e g (G) = 5 .$
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