Two bodies of mass 1 kg and 3 kg have position vector (i ∧+2 j ∧+k ∧) and (-3 i-2 j+k) respect

step 1 My question is two bodies of mass M, 1kG and 3kG have position vectors. These are given respecti

Two bodies of mass 1 kg and 3 kg have position vector (i...

Two bodies of mass $1 \mathrm{~kg}$ and $3 \mathrm{~kg}$ have position vector $(\mathrm{i} \wedge+2 \mathrm{j} \wedge+\mathrm{k} \wedge)$ and $(-3 \mathrm{i}-2 \mathrm{j}+\mathrm{k})$ respectively the centre of mass of this system has a position vector ..... $\{\mathrm{A}\}-2 \mathrm{i} \wedge+2 \mathrm{k} \wedge$ $\{B\}-2 i \wedge-j \wedge+k \wedge$ $\{C\} 2 i \wedge-j \wedge-k \wedge$ $\{\mathrm{D}\}-\mathrm{i} \wedge+\mathrm{j} \wedge+\mathrm{k} \wedge$

Two bodies of mass $1 \mathrm{~kg}$ and $3 \mathrm{~kg}$ have position vector $(\mathrm{i} \wedge+2 \mathrm{j} \wedge+\mathrm{k} \wedge)$ and $(-3 \mathrm{i}-2 \mathrm{j}+\mathrm{k})$ respectively the centre of
mass of this system has a position vector .....
$\{\mathrm{A}\}-2 \mathrm{i} \wedge+2 \mathrm{k} \wedge$
$\{B\}-2 i \wedge-j \wedge+k \wedge$
$\{C\} 2 i \wedge-j \wedge-k \wedge$
$\{\mathrm{D}\}-\mathrm{i} \wedge+\mathrm{j} \wedge+\mathrm{k} \wedge$

Key Concepts

Vector Arithmetic

Vector arithmetic involves operations such as addition, subtraction, and multiplication by scalars on vectors. It is crucial for combining multiple position vectors when determining the resultant vector, such as when computing the center of mass of a system by aggregating weighted contributions from each mass.

Center of Mass

The center of mass is a point representing the average location of the mass in a system. In physics, it is calculated as the weighted average of the positions of all particles, where the weights are the masses of the particles. This concept is essential in analyzing the motion of a system as if all the mass were concentrated at this single point.

Position Vector

A position vector represents the location of a point in space relative to an origin. It is typically expressed in terms of its components along the axes of a coordinate system. Understanding position vectors is fundamental when locating objects or calculating distances and directions in both physics and mathematics.

Weighted Average

A weighted average is a mean in which each quantity to be averaged is assigned a weight reflecting its importance. In the context of the center of mass, the position vectors of the masses are averaged with weights corresponding to their mass values, allowing for a precise determination of the overall system's balance point.

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