Lösungen

1

v={2,3}; v1={-2,4}; v2={2,1};
gl=(v == λ v1+ μ v2)

Solve[gl,{λ,μ}]

%//N

2

Det[{v1,v2}]

3

d[α_]:= {{Cos[α Degree],-Sin[α Degree]},{Sin[α Degree],Cos[α Degree]}};
d[45].{0,1}

d[45].{1,0}

d[90].v//N

d[18].v//N

4

a

g[t_]:=v1+t(v2-v1)

solv1=Solve[x==g[t][[1]],{t}]//Flatten

Remove[y]

y-g[t][[2]]/.solv1 //Simplify

n={3/4,1}

vLen[v_]:=Sqrt[v.v]; vLen[n]

(-(5/2) + ((3 x)/4) + y)/vLen[n]  // Simplify

Abstand gO = - 2

ϕ[x_, y_, d_] := (d + ((3 x)/4) + y)/vLen[n]  // 
        Simplify

Solve[ϕ[2,3,d]==0,{d}]

ϕ[x,y,-9/2]

Abstand qO = -18/5

differenz = -18/5-(-2)

%//N

b

n1= n/vLen[n]

n1= differenz n/vLen[n] // N

5

a

v1={-2,4,1}; v2={2,1,3}; v3={2,3,-1};
Cross[v1,v2]

b

vLen[Cross[v1,v2]]

vLen[Cross[v1,v2]]//N

c

Det[{v1,v2,v3}]

d

Det[{v1,v2,v3}]/vLen[Cross[v1,v2]]

Det[{v1,v2,v3}]/vLen[Cross[v1,v2]]//N

e

Solve[v3==λ v1+ μ v2,{λ,μ}]

Keine Lösung