A 5.00 kg mass is located at (1.0 m, 0.00 m, 3.00 m), a 2.00 kg mass is located at (0.00 m, 3.00 m, −2.00 m), and a 3.00 kg mass is located at (−1.0 m , −2.00 m , 0.00 m). The center of gravity of the system of masses is

The center of gravity of a system of masses is calculated by finding the weighted average of the positions of the masses, where the weights are the masses themselves.

The x-coordinate of the center of gravity is given by (m1x1 + m2x2 + m3*x3) / (m1 + m2 + m3), where m1, m2, and m3 are the masses and x1, x2, and x3 are the x-coordinates of the masses.

Substituting the given values, we get (5.00 kg * 1.0 m + 2.00 kg * 0.00 m + 3.00 kg * -1.0 m) / (5.00 kg + 2.00 kg + 3.00 kg) = 0.00 m.

Similarly, the y-coordinate of the center of gravity is given by (m1y1 + m2y2 + m3*y3) / (m1 + m2 + m3). Substituting the given values, we get (5.00 kg * 0.00 m + 2.00 kg * 3.00 m + 3.00 kg * -2.00 m) / (5.00 kg + 2.00 kg + 3.00 kg) = 0.00 m.

Finally, the z-coordinate of the center of gravity is given by (m1z1 + m2z2 + m3*z3) / (m1 + m2 + m3). Substituting the given values, we get (5.00 kg * 3.00 m + 2.00 kg * -2.00 m + 3.00 kg * 0.00 m) / (5.00 kg + 2.00 kg + 3.00 kg) = 1.00 m.

So, the center of gravity of the system of masses is at (0.00 m, 0.00 m, 1.00 m).