Let the sides of the triangle be represented by the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\).

\(\vec{a} = 2\hat{i} - \hat{j} + \hat{k}\)

\(\vec{b} = \hat{i} - 3\hat{j} - 5\hat{k}\)

\(\vec{c} = -3\hat{i} + 4\hat{j} + 4\hat{k}\)

Find the magnitudes of the vectors:

\(|\vec{a}| = \sqrt{2^2 + (-1)^2 + 1^2} = \sqrt{4 + 1 + 1} = \sqrt{6}\)

\(|\vec{b}| = \sqrt{1^2 + (-3)^2 + (-5)^2} = \sqrt{1 + 9 + 25} = \sqrt{35}\)

\(|\vec{c}| = \sqrt{(-3)^2 + 4^2 + 4^2} = \sqrt{9 + 16 + 16} = \sqrt{41}\)

Check if the triangle is right-angled by verifying the Pythagorean theorem:

\(|\vec{a}|^2 + |\vec{b}|^2 = 6 + 35 = 41\)

\(|\vec{c}|^2 = 41\)

Since \(|\vec{a}|^2 + |\vec{b}|^2 = |\vec{c}|^2\), the triangle is right-angled.