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The position vectors of three particles ...

The position vectors of three particles of mass `m_(1) = 1kg, m_(2) = 2kg and m_(3) = 3kg` are `r_(1) = ((hat(i) + 4hat(j) +hat(k))`m, `r_(2) = ((hat(i)+(hat(j)+hat(k))`m and `r_(3) = (2hat(i) - (hat(j) -(hat(2k))`m, respectively. Find the position vector of their center of mass.

Text Solution

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The position vector of centre of mass of the three particles is given by
`vec(r )_(c )=(m_(1)vec(r )_(1)+m_(2)vec(r )_(2)+m_(3) vec(r )_(3))/(m_(1)+m_(2)+m_(3))`
`vec(r )_(c )=(1(hat(i)+4hat(j)+hat(k))+2(hat(i)+hat(j)+hat(k))+4(2hat(i)-hat(j)-2hat(k)))/(1+2+4)`
` = ((11hat(i)+2hat(j)-5hat(k)))/(7)=(1)/(7)(11hat(i)+2hat(j)-5hat(k))m`
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