Lösungen

1

a={3,2}; b={2,3}; c[x_]:={x,2};
solv=Solve[c[x]==3 a + λ b,{x,λ}] // Flatten

<<Graphics`Arrow`

Show[Graphics[{Arrow[{0, 0},a], Arrow[{0, 0},b]}]];

Show[Graphics[{Arrow[{0, 0},a],Arrow[{0, 0},b],
Line[{c[19/3],3 a}],Line[{c[19/3],- 4/3 b}],
    Hue[0], Arrow[{0, 0},c[19/3]],
    Arrow[{0, 0},3 a], Arrow[{0, 0},- 4/3 b]}]];

2

180 Degree//N

p1={2,5}; p2={-1,-4}; d={{Cos[30 Degree], Sin[30 Degree]},{-Sin[30 Degree],Cos[30 Degree]}};
{1,0}.d

(p1-p2).d + p2

%//N

3

p1={1,3,2}; p2={4,1,3}; p3={2,5,4}; p4={8,9,7};

Det[{p4-p1,p3-p1,p2-p1}]

Det[{p4-p1,p3-p1,p2-p1}]/6

%//N

4

5

6