Position and Displacement Vectors

A position vector describes an object's location relative to a reference point, typically the origin. Displacement vector represents the change in position—the straight-line distance and direction from an initial to final location. While position is absolute, displacement depends only on start and end points, not the path taken.

A position vector is drawn from the origin to the object's location using coordinate components. In 2D, it's expressed as r = xi + yj, where x and y are distances along horizontal and vertical axes. In 3D, add a z-component: r = xi + yj + zk, with unit vectors i, j, k indicating direction.

Displacement measures only the net change in position from start to finish, regardless of route. Distance traveled sums all path segments. An object moving in a circle returns to its starting point with zero displacement but nonzero distance. This distinction is crucial for analyzing motion accurately.

Displacement is found by subtracting the initial position vector from the final position vector: Δr = r_final − r_initial. This vector subtraction yields a single vector pointing from start to end. The magnitude gives distance between positions; direction shows the net motion path.

Vector quantities like position and displacement include both magnitude and direction, essential for complete motion description. Scalars alone cannot specify where an object is or how it moved. Vectors enable precise spatial representation and allow calculations of velocity, acceleration, and forces acting on moving objects.

Displacement can be negative when motion occurs opposite to the chosen positive direction. In 1D, negative displacement indicates movement toward decreasing coordinate values. The sign conveys direction relative to the reference frame, making it essential for tracking motion along a line or axis.