Lösungen/Solutions/
F1S1Ue/Ex9

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

Ueb/Ex 1      W

op1 = {1, 4, 2}; va = {1, 3, 2};  vb = {1, 1, -2};  
    vc  = {3, 2, -12};

a) l.a. / l.d.

Solve[x va + y vb + z vc == {0, 0, 0}, {x, y, z}] // 
      Flatten

b)

op1  +  (-1) va

op1  -  vb

op1  -  vc

c)

vecLen[v_] := {Sqrt[v . v], "or num.", N[Sqrt[v . v]]}

vecLen[va]

vecLen[vb]

vecLen[vc]

d)

p1p7 = vecLen[va + vb + vc]

p5p3 = vecLen[va + vb - vc]

p2p8 = vecLen[-va + vb + vc]

p4p6 = vecLen[va - vb + vc]

Ueb/Ex 2      W

b1 = {1, 2};  b2 = {-1, 2};  a = {1, 3};  
    b = {-1, 4}; 
e1 = {1, 0};   e2 = {0, 
        1};

vB  = x1 e1  +  x2 e2

vBnew  = y1 b1  +  y2 b2

Solve[a  == y1 b1  +  y2 b2, {y1, y2}]

Solve[b  == y1 b1  +  y2 b2, {y1, y2}]

Solve[a + b  == y1 b1  +  y2 b2, {y1, y2}]

vecLen[v_] := {Sqrt[v . v], "or num.", N[Sqrt[v . v]]}

vecLen[a + b]

Ueb/Ex 3      W

e1new

e1new = {Cos[30/360 2  Pi], Sin[30/360 2  Pi]}

vecLen[e1new]

e2new

e2new =  {-e1new[[2]], e1new[[1]]}

v

vB = x1 e1  +  x2 e2

vBnew = y1 e1new + y2 e2new

Solve[vB == vBnew, {y1, y2}]