Two bodies of mass `1 kg` and `3 kg` have position vectors `hat i+ 2 hat j + hat k` and `- 3 hat i- 2 hat j+ hat k`, respectively. The centre of mass of this system has a position vector.

Options

A. `-2hat(i)+2hat(k)`
B. `-2hat(i)-hat(j)+hat(k)`
C. `2hat(i)-hat(j)-hat(k)`
D. `-hat(i)+hat(j)+hat(k)`

Answer

B

Explanation

`vec(r)_(CM)=(m_(1)vec(r)_(1)+m_(2)vec(r)_(2))/(m_(1)+m_(2))=(1(hat(i)+2hat(j)+hat(k))+3(-3hat(i)-2hat(j)+hat(k)))/(4)`
`vec(r)_(CM)=(-8hat(i)-4hat(j)+4hat(k))/(4)`
`vec(r)_(CM)=-2hat(i)-hat(j)+hat(k)`