AB =
\((\sqrt{{(1-2)^{2}}+(-1+4)^{2}+(3-5)^{2}}\\=\sqrt{1+9+4}\\=\sqrt{14}\)
BC =
\((\sqrt{{(2-5)^{2}}+(-4+13)^{2}+(5-11)^{2}}\\=\sqrt{9+81+36}\\=3\sqrt{14}\)
CA =
\((\sqrt{{(5-1)^{2}}+(-13+1)^{2}+(11-3)^{2}}\\=\sqrt{16+144+64}\\=\sqrt{224}=4\sqrt{14}\)
Since AB + BC = CA ∴ A, B, C are collinear