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# Two particles of masses 1 kg and 3 kg have velocities $(2 \hat i-3 \hat j+4 \hat k)ms^{-1}$ and $(4 \hat {i}+2 \hat j+\hat k)ms^{-1}$ at a given instant of time. The velocity of the center of mass is

$\begin {array} {1 1} (a)\;3.5 \hat{i}+2.25 \hat{j}+1.75 \hat {k} \;m/s\\ (b)\;3.5 \hat{i}-2.25 \hat{j}+1.75 \hat {k} \;m/s \\ (c)\;2.5 \hat{i}+2.25 \hat{j}+1.75 \hat {k} \;m/s \\(d)\;3.5 \hat{i}+0.75 \hat{j}+1.75 \hat {k} \;m/s \end {array}$

$\bar {V}cm=\large\frac{m_1\overrightarrow{v_1}+m_2 \overrightarrow {v_2}}{m_1+m_2}$
$\qquad= \large\frac{1(2 \hat {i}-3 \hat {j}+4 \hat {k})+3 (4 \hat {i}+2 \hat j+\hat {k})}{4}$
$\qquad= 3.5 \hat {i}+0.75 \hat i+1.75\hat k\;m/s$