The centre of mass of a system of three particles of masses \( 1 g, 2 g \) and \( 3 g \) is take...

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The centre of mass of a system of three particles of masses \( 1 g, 2 g \) and \( 3 g \) is taken as the origin of a coordinate system. The position vector of a fourth particle of mass \( 4 \mathrm{~g} \) such that the centre of mass of the four particle system lies at the point \( (1,2,3) \) is \( \alpha(\hat{i}+2 \hat{j}+3 \hat{k}) \), where \( \alpha \) is a constant. The value of \( \alpha \) is
[AMU (Med.) 2010]
(a) \( 10 / 3 \)
(b) \( 5 / 2 \)
(c) \( 1 / 2 \)
(d) \( 2 / 5 \)
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