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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 point M in the case where g(G)=5.

$${g}\left({M}\right)=\mathrm{2}{M}\overset{\rightarrow} {{B}}.{M}\overset{\rightarrow} {{C}}+{M}\overset{\rightarrow} {{C}}.{M}\overset{\rightarrow} {{A}}+{M}\overset{\rightarrow} {{A}}.{M}\overset{\rightarrow} {{B}} \\ $$$${g}\left({G}\right)=\mathrm{4}{MA}^{\mathrm{2}} +\mathrm{3}{M}\overset{\rightarrow} {{A}}\left({A}\overset{\rightarrow} {{B}}+{A}\overset{\rightarrow} {{C}}\right) \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{show}\:{that}\:\forall\:{M}\:\in\:{plan} \\ $$$${g}\left({M}\right)={g}\left({G}\right)+\mathrm{4}{MG}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{Determine}\:{the}\:{set}\:{of}\:{point}\:{M}\:{of}\:{plan} \\ $$$${such}\:{as}\:{g}\left({M}\right)={g}\left({A}\right) \\ $$$$\left.\mathrm{2}\right)\:{Construct}\:{this}\:{set}\:{of}\:{point}\:{M} \\ $$$${in}\:{the}\:{case}\:{where}\:{g}\left({G}\right)=\mathrm{5}. \\ $$

Question Number 81498 Answers: 1 Comments: 0

what the formula a^ × (b^ ×c^ ) ?

$$\mathrm{what}\:\mathrm{the}\:\mathrm{formula} \\ $$$$\bar {\mathrm{a}}\:×\:\left(\bar {\mathrm{b}}×\bar {\mathrm{c}}\right)\:? \\ $$

Question Number 81295 Answers: 1 Comments: 2

what is vector unit orthogonal to (1,2,−2) and parallel to yz−plane?

$${what}\:{is}\:{vector}\:{unit}\:{orthogonal} \\ $$$${to}\:\left(\mathrm{1},\mathrm{2},−\mathrm{2}\right)\:{and}\:{parallel}\:{to}\: \\ $$$${yz}−{plane}? \\ $$

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(a^ ×b^ ).c^ = (a×c) . (b×c). it right?

$$\left(\bar {{a}}\:×\bar {{b}}\:\right).\bar {{c}}\:=\:\left({a}×{c}\right)\:.\:\left({b}×{c}\right).\:{it}\:{right}? \\ $$

Question Number 81007 Answers: 0 Comments: 1

if t_m +t_n and t_m −t_n is triangular number find the value of m+n

$${if}\:\:\:{t}_{{m}} +{t}_{{n}} \:{and}\:{t}_{{m}} −{t}_{{n}} \:{is}\:{triangular} \\ $$$${number}\:{find}\:{the}\:{value}\:{of}\:{m}+{n} \\ $$

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Determine the set of points M such as ∣∣MA^→ +MB^→ +2MC^→ ∣∣=6(√3) AB=BC=AC=6 ABC is triangle.

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:\mathrm{M}\: \\ $$$$\mathrm{such}\:\mathrm{as}\:\mid\mid\mathrm{M}\overset{\rightarrow} {\mathrm{A}}+\mathrm{M}\overset{\rightarrow} {\mathrm{B}}+\mathrm{2M}\overset{\rightarrow} {\mathrm{C}}\mid\mid=\mathrm{6}\sqrt{\mathrm{3}} \\ $$$$\mathrm{AB}=\mathrm{BC}=\mathrm{AC}=\mathrm{6} \\ $$$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{triangle}. \\ $$

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if I_n =∫_0 ^(π/4) tan^n xdx and I_n =a_n +b_n I_(n−2) then find a_(10)

$${if}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {tan}^{{n}} {xdx}\:{and}\:{I}_{{n}} ={a}_{{n}} +{b}_{{n}} {I}_{{n}−\mathrm{2}} \:{then}\:{find}\:{a}_{\mathrm{10}} \\ $$

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the circle represents a farm where (LK) is symetric axe of circle such as ∀ M of this circle verifying ML^2 −4MK^2 =0 with LK=150m. calculate the radius of circle. please help me...

$$\mathrm{the}\:\mathrm{circle}\:\mathrm{represents}\:\mathrm{a}\:\mathrm{farm}\:\mathrm{where} \\ $$$$\left(\mathrm{LK}\right)\:\mathrm{is}\:\mathrm{symetric}\:\mathrm{axe}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{such} \\ $$$$\mathrm{as}\:\forall\:\mathrm{M}\:\mathrm{of}\:\mathrm{this}\:\mathrm{circle}\:\mathrm{verifying} \\ $$$$\mathrm{ML}^{\mathrm{2}} −\mathrm{4MK}^{\mathrm{2}} =\mathrm{0}\:\:\mathrm{with}\:\mathrm{LK}=\mathrm{150m}. \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle}. \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}... \\ $$

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Question Number 77745 Answers: 0 Comments: 1

ABC is any triangle. C′ . B′ .A′ are respectively middles of [AB] . [AC] and [BC]. we suppose that AB=c AC=b BC=a. 1) u^(→ ) =a^2 BC^→ +b^(2 ) C^→ A+c^2 AB^→ is a vector Demonstrate that u^→ =(a^2 −b^2 )AC^→ +(c^2 −a^2 )AB^→ . i have done it. 2)Deduct that u^→ is not a null vector.

$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{any}\:\mathrm{triangle}. \\ $$$$\mathrm{C}'\:.\:\mathrm{B}'\:\:.\mathrm{A}'\:\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{middles} \\ $$$$\mathrm{of}\:\left[\mathrm{AB}\right]\:.\:\left[\mathrm{AC}\right]\:\:\mathrm{and}\:\:\left[\mathrm{BC}\right]. \\ $$$$\mathrm{we}\:\mathrm{suppose}\:\mathrm{that}\: \\ $$$$\mathrm{AB}=\mathrm{c}\:\:\:\mathrm{AC}=\mathrm{b}\:\:\:\:\mathrm{BC}=\mathrm{a}. \\ $$$$\left.\mathrm{1}\right)\:\overset{\rightarrow\:} {\mathrm{u}}=\mathrm{a}^{\mathrm{2}} \mathrm{B}\overset{\rightarrow} {\mathrm{C}}+\mathrm{b}^{\mathrm{2}\:} \overset{\rightarrow} {\mathrm{C}A}+\mathrm{c}^{\mathrm{2}} \mathrm{A}\overset{\rightarrow} {\mathrm{B}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{u}}=\left(\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \right)\mathrm{A}\overset{\rightarrow} {\mathrm{C}}+\left(\mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} \right)\mathrm{A}\overset{\rightarrow} {\mathrm{B}}. \\ $$$${i}\:{have}\:{done}\:{it}. \\ $$$$\left.\mathrm{2}\right){D}\mathrm{educt}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{u}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{null}\:\mathrm{vector}. \\ $$

Question Number 77676 Answers: 0 Comments: 0

Please how can we demonstrate that a vector is null... hello

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{can}\:\mathrm{we}\:\mathrm{demonstrate} \\ $$$$\mathrm{that}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{is}\:\mathrm{null}... \\ $$$$\mathrm{hello} \\ $$

Question Number 77356 Answers: 1 Comments: 0

The plan is provided with an orthonormal reference ( O.I.J). the following points are given A(1,2) B(−2,3) C(1,9). We assume that the point O is the barycenter of the point A,B,C. →O=bar{(A;3),(B;1),(C;−1)} Question 1 knowing that 3MA^2 +MB^2 −MC^2 =3MO^2 +3OA^2 +OB^2 −OC^2 Determine and construct the set of points M on the plane such as 3MA^2 +MB^2 −MC^2 =−42

$$\mathrm{The}\:\mathrm{plan}\:\mathrm{is}\:\mathrm{provided}\:\mathrm{with}\:\mathrm{an}\: \\ $$$$\mathrm{orthonormal}\:\mathrm{reference}\:\left(\:\mathrm{O}.\mathrm{I}.\mathrm{J}\right). \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{We}\:\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{barycenter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{A},\mathrm{B},\mathrm{C}. \\ $$$$\rightarrow\mathrm{O}=\mathrm{bar}\left\{\left(\mathrm{A};\mathrm{3}\right),\left(\mathrm{B};\mathrm{1}\right),\left(\mathrm{C};−\mathrm{1}\right)\right\} \\ $$$$ \\ $$$$\mathrm{Question}\:\mathrm{1} \\ $$$$\mathrm{knowing}\:\mathrm{that} \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =\mathrm{3MO}^{\mathrm{2}} +\mathrm{3OA}^{\mathrm{2}} +\mathrm{OB}^{\mathrm{2}} −\mathrm{OC}^{\mathrm{2}} \\ $$$$\mathrm{Determine}\:\mathrm{and}\:\mathrm{construct}\:\mathrm{the}\:\mathrm{set}\: \\ $$$$\mathrm{of}\:\mathrm{points}\:\mathrm{M}\:\mathrm{on}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{such}\:\mathrm{as} \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =−\mathrm{42} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 77296 Answers: 0 Comments: 4

Determiner et construire l.ensemble des points M tel que: 3MA^2 +MB^2 −MC^2 =−42 Le plan est muni d.un repere orthonorme (O,I,J) A(1,2) B(−2,3) C(1,9). on considere que O=barycentre{(A,3);(B;1);(C;−1)}

$$\mathrm{Determiner}\:\mathrm{et}\:\mathrm{construire}\:\mathrm{l}.\mathrm{ensemble} \\ $$$$\mathrm{des}\:\mathrm{points}\:\mathrm{M}\:\mathrm{tel}\:\mathrm{que}: \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =−\mathrm{42} \\ $$$$\mathrm{Le}\:\mathrm{plan}\:\mathrm{est}\:\mathrm{muni}\:\mathrm{d}.\mathrm{un}\:\mathrm{repere}\: \\ $$$$\mathrm{orthonorme}\:\left(\mathrm{O},\mathrm{I},\mathrm{J}\right) \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\:\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{on}\:\mathrm{considere}\:\mathrm{que}\: \\ $$$$\mathrm{O}=\mathrm{barycentre}\left\{\left(\mathrm{A},\mathrm{3}\right);\left(\mathrm{B};\mathrm{1}\right);\left(\mathrm{C};−\mathrm{1}\right)\right\} \\ $$

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