TeM

A=vector((0,2,5)); B=vector((2,3,0)); C=vector((3,0,0)); ab=B-A; ac=C-A; fab = ab/abs(ab)*2.4; fac = (ac/abs(ac))*(fab.dot_product(ac)/abs(ac)); print "Seilkraft: %f" % abs(fab); print "Komponente in Richtung AC: %f" % abs(fac); P =arrow3d(A, A+ab); P+=arrow3d(A, A+fab, color=(1,0,0)); P+=arrow3d(A, A+ac); P+=arrow3d(A, A+fac, color=(1,0,0)); P+=line3d([(0,0,0), (5,0,0)]); P+=line3d([(0,0,0), (0,5,0)]); P+=line3d([(0,0,0), (0,0,5)]); P.show(); 

Seilkraft: 2.400000
Komponente in Richtung AC: 2.061374

Seilkraft: 2.400000
Komponente in Richtung AC: 2.061374

def unit(v): return v/abs(v) var('a, F, F1, F2, F3') S1=F1*unit(vector((-a, -2*a, -2*a))) S2=F2*unit(vector((a, -2*a, -2*a))) S3=F3*unit(vector((0, 0, -2*a))) S=vector((0,F*a,0)) s = solve(S1 + S2 + S3 + S, (F1, F2, F3)) #s = solve([a == b for a, b in zip(S1 + S2 + S3 + S, vector((0,0,0)))], F1, F2, F3) show(s) 

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[F_{1} = \frac{3}{4} \, \sqrt{a^{2}} F, F_{2} = \frac{3}{4} \, \sqrt{a^{2}} F, F_{3} = -\sqrt{a^{2}} F\right]\right]

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[F_{1} = \frac{3}{4} \, \sqrt{a^{2}} F, F_{2} = \frac{3}{4} \, \sqrt{a^{2}} F, F_{3} = -\sqrt{a^{2}} F\right]\right]