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The position vectors of two point masses...

The position vectors of two point masses 10 kg and 5 kg are `(-3vec(i)+2vec(j)+4vec(k))m " and " (3vec(i)+6vec(j)+5vec(k))m` respectively. Locate the position of centre of mass.

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`m_(1)=10kg, m_(2)=5kg`
`vec(r)_(1)=(-3hat(i)+2hat(j)+4hat(j))m`
`vec(r)_(2)=(3hat(i)+6hat(j)+5hat(k))m`
`vec(r)=(m_(1)vec(r_(1))+m_(2)vec(r_(2)))/(m_(1)+m_(2))`
`vec(r)=(10(-3hat(i)+2hat(j)+4hat(k))+5(3hat(i)+6hat(j)+5hat(k)))/(10+5)`
`" "=(-30hat(i)+20hat(j)+40hat(k)+15hat(i)+30hat(j)+25hat(k))/15`
`" "=(-15hat(i)+50hat(j)+65hat(k))/15`
`vec(r)=(-hat(i)+10/3hat(j)+13/3hat(k))m`
The center of mass is located at position `vec(r)`
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