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in [tex]R^3[/tex] we have vector field [tex]X[/tex] and for every point [tex]p(x,y,z)[/tex] in [tex]R^3[/tex] space, vector field [tex]X(p) = (p; X_x(p), X_y(p), X_z(p))[/tex] has:

[tex]X_x(p) = -x+y+z[/tex]

[tex]X_y(p) = x-y+z[/tex]

[tex]X_z(p) = x+y-z[/tex]

Find integral curve [tex]\alpha[/tex] of this vector field and it should pass through point [tex]$q=(a,b,c) \in R^3[/tex] so that [tex]\alpha(0)=q[/tex].

Thanks for any advise.