The centroid (or center of mass) of a collection of n objects with masses m1, m2,m3, …, mn...

The centroid (or center of mass) of a collection of n objects with masses m1, m2,m3, …, mn and respective position vectors a1, a2, a3, …, an is the point with position vector

Calculate the centroid of the objects with the given masses and positions.

(a) m1 = 1, m2 = 3/2, m3 = 5, m4 = 1/2; a1 = (0, 2, 0), a2 = (−7, 2, 0), a3 = (−1, −1, −1), a4 = (8, 4, −2)

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(b) m1= m2= m3 = m4 = m5 = 6; , , , a5=(0, 0,1)