Lösungen T E+M Alg 1 05 1

1

vO={0,0,0};vA={4,3,0};vB={6,5,0};vC={2,8,0};
{Cross[vA,vB],Cross[vB,vC],Cross[vC,vA],Cross[vA,vB]+Cross[vB,vC]+Cross[vC,vA]}

Umlausinn ändern: Negativ

2

k1={1,5,6};k1=k1/Norm[k1];k2={2,5,7};k2=k2/Norm[k1];k1+k2

%//N

a={3,1,0};b={0,2,1};c={1,0,4};
solv=Solve[k1+k2 == λ a + μ b + ν c, {λ,μ,ν}] //Flatten

%//N

λ a/.solv[[1]]

%//N

Norm[%]

Norm[%%%]

3

a

vA={1,5,6};vB={2,5,7};vC={3,1,0};vD={1,0,4};

V=Det[{vB-vA,vC-vA,vD-vA}]/6

N[%]

b

(Norm[Cross[vB-vA,vD-vA]]+Norm[Cross[vC-vB,vD-vB]]+Norm[Cross[vB-vA,vC-vA]]+Norm[Cross[vC-vA,vD-vA]])/2

N[%]

c

winkel=ArcCos[(vA-vB).(vC-vB)/(Norm[vA-vB] Norm[vC-vB])]

%//N

%/Degree

4

a

vA={4,5,-6};vB={6,2,-5};vC={2,16,1};
vX[λ_]:=vB+λ(vC-vB);
(vC-vB).(vA-vX[λ])==0

solv= Solve[(vC-vB).(vA-vX[λ])==0,{λ}]//Flatten

%//N

vX0=vX[λ]/.solv

%//N

b   ==> ausserhalb - x-Koordinaten vergleichen....

g[μ_]:=vA+ μ (vA-vX0);
g[μ][[3]]==0

solv=Solve[g[μ][[3]]==0,{μ}]//Flatten

g[μ]/.solv

%//N