1. **Stating the problem:** We are given a rectangular prism (balok) with vertices labeled as follows: - Bottom face: P, Q, R, S - Top face: T, U, V, W We need to find the vector expression: $$\overrightarrow{TW} - \overrightarrow{QS} + \overrightarrow{UV}$$ 2. **Understanding the vectors:** - $\overrightarrow{TW}$ is the vector from point T to point W. - $\overrightarrow{QS}$ is the vector from point Q to point S. - $\overrightarrow{UV}$ is the vector from point U to point V. 3. **Assigning coordinates for clarity:** Assume the rectangular prism is axis-aligned with: - $P = (0,0,0)$ (bottom-front-left) - $Q = (a,0,0)$ (bottom-front-right) - $R = (a,b,0)$ (bottom-back-right) - $S = (0,b,0)$ (bottom-back-left) - $T = (0,0,c)$ (top-front-left) - $U = (a,0,c)$ (top-front-right) - $V = (a,b,c)$ (top-back-right) - $W = (0,b,c)$ (top-back-left) 4. **Calculate each vector:** - $$\overrightarrow{TW} = W - T = (0,b,c) - (0,0,c) = (0,b,0)$$ - $$\overrightarrow{QS} = S - Q = (0,b,0) - (a,0,0) = (-a,b,0)$$ - $$\overrightarrow{UV} = V - U = (a,b,c) - (a,0,c) = (0,b,0)$$ 5. **Substitute into the expression:** $$\overrightarrow{TW} - \overrightarrow{QS} + \overrightarrow{UV} = (0,b,0) - (-a,b,0) + (0,b,0)$$ 6. **Simplify step-by-step:** $$= (0,b,0) + (a,-b,0) + (0,b,0)$$ $$= (0 + a + 0, b - b + b, 0 + 0 + 0)$$ $$= (a, b, 0)$$ 7. **Final answer:** $$\boxed{(a,b,0)}$$ This vector points from the origin along the length $a$ in the x-direction and width $b$ in the y-direction, lying on the bottom face of the prism.