1. The problem asks to draw vectors with angles 120°, 240°, and 360° using the head-to-tail method and polygon representation. 2. Vectors can be represented graphically by arrows starting from the origin or from the head of the previous vector (head-to-tail). 3. The angle of a vector is measured counterclockwise from the positive x-axis. 4. For each vector, we can write its components using the formulas: $$x = r \cos(\theta)$$ $$y = r \sin(\theta)$$ where $r$ is the magnitude (assumed 1 for simplicity) and $\theta$ is the angle in degrees. 5. Calculate components: - For 120°: $x = \cos(120^\circ) = -\frac{1}{2}$, $y = \sin(120^\circ) = \frac{\sqrt{3}}{2}$ - For 240°: $x = \cos(240^\circ) = -\frac{1}{2}$, $y = \sin(240^\circ) = -\frac{\sqrt{3}}{2}$ - For 360°: $x = \cos(360^\circ) = 1$, $y = \sin(360^\circ) = 0$ 6. Using the head-to-tail method, place the tail of the second vector at the head of the first, and the tail of the third at the head of the second. 7. The polygon formed by connecting the vectors head-to-tail represents their sum. Final answer: The vectors with angles 120°, 240°, and 360° can be represented graphically by arrows with components calculated above, arranged head-to-tail to form a polygon illustrating vector addition.