### a system consist of particles of masses 5, 2 and 3g located at (1, 0,...

a system consist of particles of masses 5, 2 and 3g located at (1, 0, -1), (1, 2, 1) and (1, 1, 3) respectively. find the center of position of masses?

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Let 5, 2, 3 be masses m1, m2 ; m3
Let (x, y, z) be the form of the positions (1, 0, -1), (1, 2, 1) and (1, 1, 3) for m1, m2 and m3 respectively.
Also, let Cx, Cy, Cz and Cav. be centres of masses, x, y, z and average.

Cx= (m1x1 + m2x2 + m3x3)/(x1 + x2 + x3)
= (5•1 + 2•1 + 3•1)/(1 + 1 + 1)
= (5 + 2 + 3)/(3)
= 10/3

Cy= (m1y1 + m2y2 + m3y3)/(y1 + y2 + y3)
= (5•0 + 2•2 + 3•1)/(0 + 2 + 1)
= (4 + 3)/(3)
= 7/3

Cz= (m1z1 + m2z2 + m3z3)/(z1 + z2 + z3)
= (5•-1 + 2•1 + 3•3)/(-1 + 1 + 3)
= (-5 + 2 + 9)/(3)
= 6/3

Cav.= (Cx + Cy + Cz)/3
= (10/3 + 7/3 + 6/3)/3
= (23/3)/3
= 23/9
= 2.56
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