In \((x, y, z)\) notation, four ideal monatomic gas particles have the velocities \(\vec{v}_{1}=(-6.0,5.0,1.0) \mathrm{m} / \mathrm{s}, \vec{v}_{2}=\) \((4.0,5.0,-2.0 \mathrm{~m} / \mathrm{s}), \vec{v}_{3}=(7.0,0,8.0) \mathrm{m} / \mathrm{s}\), and \(\vec{v}_{4}=\) \((-4.0,-9.0,-6.0) \mathrm{m} / \mathrm{s}\).

(a) What is the average velocity of the particles?

(b) What is the root-mean-square speed of the particles?

(c) Why is Eq. 19. 25, \(v_{\text {rms }}^{2}=3\left(v_{x}^{2}\right)_{\text {av }}\), unlikely to give the correct answer here?