Two blocks of mass `1kg` and `3 kg` have position v ectors ` hat(i) + 2 hat(j) + hat(k)` and `3 hat(i) - 2 hat(j) + hat(k)` , respectively . The center 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)-2hat(k)`
D. `-hat(i)+hat(j)+hat(k)`

Answer

B

Explanation

The position vector of centre of mass
`bar(r)_(cm) = (m_(1)bar(r)_(1)+m_(2)bar(r)_(2))/(m_(1)+m_(2))`
` = (1(vec(i)+vec(j)+vec(k))+3(-3vec(i)-2vec(j)+vec(k)))/(1+3)`
` = 1/4 (-8vec(i) - 4vec(j)+4vec(k)) = -2vec(i)-vec(j)+vec(k)`