1. **Stating the problem:** We have a point A at the origin with three ropes extending along the positive y-axis to B (1.5 m), negative x-axis to C (2 m), and positive z-axis to D (1.5 m). We want to analyze the position vectors of points B, C, and D relative to A. 2. **Formula and rules:** The position vector of a point relative to the origin is given by $$\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$$ where $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along the x, y, and z axes respectively. 3. **Intermediate work:** - Point B lies along the positive y-axis at 1.5 m, so $$\vec{r}_B = 0\hat{i} + 1.5\hat{j} + 0\hat{k} = 1.5\hat{j}$$ - Point C lies along the negative x-axis at 2 m, so $$\vec{r}_C = -2\hat{i} + 0\hat{j} + 0\hat{k} = -2\hat{i}$$ - Point D lies along the positive z-axis at 1.5 m, so $$\vec{r}_D = 0\hat{i} + 0\hat{j} + 1.5\hat{k} = 1.5\hat{k}$$ 4. **Explanation:** Each position vector shows the displacement from point A to the respective points along the coordinate axes. The negative sign for C indicates direction along the negative x-axis. **Final answer:** $$\vec{r}_B = 1.5\hat{j}, \quad \vec{r}_C = -2\hat{i}, \quad \vec{r}_D = 1.5\hat{k}$$