Physics · Ch 2 — Kinematics

Displacement Vector in Cartesian Coordinate System

2.7.1

Displacement Vector in Cartesian Coordinate System

Writing positions as position vectors turns 'displacement' into a single vector subtraction. If a particle moves from point $P_1$ , with position vector $\vec r_1 = x_1\hat i+y_1\hat j+z_1\hat k$ , to point $P_2$ , with position vector $\vec r_2 = x_2\hat i+y_2\hat j+z_2\hat k$ , then the displacement vector is

$\Delta\vec r = \vec r_2 - \vec r_1 = (x_2-x_1)\hat i + (y_2-y_1)\hat j + (z_2-z_1)\hat k$ …

Figure 2.27Displacement vector

What this figure shows. A particle moving from point $P_1$ (position vector $\vec r_1$ ) to point $P_2$ (position vector $\vec r_2$ ); the displacement vector $\Delta\vec r = \vec r_2 - \vec r_1$ is drawn as the arrow directly from $P_1$ to …

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