The position vectors of three particles of mass m1=1 kg, m2=2 kg and m3=3 kg are r⃗1-(î|4 ĵ|

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The position vectors of three particles of mass m1=1 kg,...

The position vectors of three particles of mass $m_{1}=1 \mathrm{~kg}, m_{2}=2 \mathrm{~kg}$ and $m_{3}=3 \mathrm{~kg}$ are $\vec{r}_{1}-(\hat{i}|4 \hat{j}| \hat{k}) m, \vec{r}_{2}-(\hat{i}|\hat{j}| \hat{k}) m$ and $\vec{r}_{3}-(2 \hat{i} \quad \hat{j} \quad 2 \hat{k})$ respectively. Find the position vec- tor of their centre of mass.

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Key Concepts

Center of Mass

The center of mass is the unique point where the weighted relative position of the distributed mass sums up to zero. It is calculated as the weighted average of the position vectors of all the particles, where the weights are the masses of the particles. This point represents the effective position of the total mass of the system and is crucial in analyzing the motion or equilibrium of composite systems.

Position Vector

A position vector is a vector that denotes the location of a point in space relative to a given origin. It is typically expressed in terms of its components along the predefined coordinate axes. In problems involving multiple particles, position vectors allow for the concise representation of the spatial arrangement of these particles.

Weighted Average

A weighted average is a mean where some values contribute more than others, reflecting their significance or weight, such as mass in mechanics problems. In the context of the center of mass, the individual position vectors are multiplied by their corresponding masses, summed together, and then divided by the total mass of the system to obtain the effective average position.

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