A 5.00 kg mass is located at (2.00 m, 0.00 m, 3.00 m) and a 2.00 kg mass is located at (0.00 m, 4.00 m, –2.00 m). The center of gravity of the system of masses is

The center of gravity (also known as the center of mass) of a system of particles is the average position of all the particles, weighted by their masses. It is calculated separately for each dimension.

The formula for finding the center of gravity is:

Center of gravity = (m1r1 + m2r2 + ... + mn*rn) / (m1 + m2 + ... + mn)

where m is the mass and r is the position.

Let's calculate the center of gravity for each dimension (x, y, z) separately:

For the x-dimension: Center of gravity_x = (m1x1 + m2x2) / (m1 + m2) = (5.00 kg * 2.00 m + 2.00 kg * 0.00 m) / (5.00 kg + 2.00 kg) = 10.00 kg*m / 7.00 kg = 1.43 m

For the y-dimension: Center of gravity_y = (m1y1 + m2y2) / (m1 + m2) = (5.00 kg * 0.00 m + 2.00 kg * 4.00 m) / (5.00 kg + 2.00 kg) = 8.00 kg*m / 7.00 kg = 1.14 m

For the z-dimension: Center of gravity_z = (m1z1 + m2z2) / (m1 + m2) = (5.00 kg * 3.00 m + 2.00 kg * -2.00 m) / (5.00 kg + 2.00 kg) = 11.00 kg*m / 7.00 kg = 1.57 m

So, the center of gravity of the system of masses is at (1.43 m, 1.14 m, 1.57 m).