3. Draw a scale diagram for these vectors and give a resultant vector 3.5mW4.2mN 7.1kmS8.6kmE

**1. 3.5 m West, 4.2 m North**<br /><br />* **Scale:** Let's choose a scale of 1 cm = 1 m. This means a 3.5 m vector will be represented by a 3.5 cm line, and a 4.2 m vector will be represented by a 4.2 cm line.<br /><br />* **Diagram:**<br /> 1. Draw a horizontal line 3.5 cm long pointing to the left (West). Label this vector A.<br /> 2. Starting at the end of vector A, draw a vertical line 4.2 cm long pointing upwards (North). Label this vector B.<br /> 3. Draw a line connecting the starting point of vector A to the endpoint of vector B. This is your resultant vector (R).<br /><br />* **Resultant Vector (Graphical Method):** Measure the length of vector R with a ruler. Let's say you measure it to be approximately 5.5 cm. Based on our scale, this represents a magnitude of 5.5 m. Use a protractor to measure the angle θ that R makes with the westward direction (vector A). This angle will be measured counter-clockwise from West. Let's say you measure it to be approximately 50°. Therefore, the resultant vector is approximately 5.5 m at 50° North of West.<br /><br />* **Resultant Vector (Calculation):**<br /> * **Magnitude:** Use the Pythagorean theorem: R = √(A² + B²) = √(3.5² + 4.2²) ≈ 5.46 m<br /> * **Direction:** Use trigonometry: tan(θ) = B/A = 4.2/3.5 => θ = arctan(4.2/3.5) ≈ 50.2° North of West<br /><br />**2. 7.1 km South, 8.6 km East**<br /><br />* **Scale:** Let's choose a scale of 1 cm = 2 km. This means a 7.1 km vector will be represented by a 3.55 cm line, and an 8.6 km vector will be represented by a 4.3 cm line.<br /><br />* **Diagram:**<br /> 1. Draw a vertical line 3.55 cm long pointing downwards (South). Label this vector C.<br /> 2. Starting at the end of vector C, draw a horizontal line 4.3 cm long pointing to the right (East). Label this vector D.<br /> 3. Draw a line connecting the starting point of vector C to the endpoint of vector D. This is your resultant vector (R).<br /><br />* **Resultant Vector (Graphical Method):** Measure the length of vector R with a ruler. Let's say you measure it to be approximately 5.6 cm. Based on our scale (1 cm = 2 km), this represents a magnitude of 11.2 km. Use a protractor to measure the angle θ that R makes with the southward direction (vector C). This angle will be measured clockwise from South. Let's say you measure it to be approximately 51°. Therefore, the resultant vector is approximately 11.2 km at 51° East of South.<br /><br />* **Resultant Vector (Calculation):**<br /> * **Magnitude:** Use the Pythagorean theorem: R = √(C² + D²) = √(7.1² + 8.6²) ≈ 11.16 km<br /> * **Direction:** Use trigonometry: tan(θ) = D/C = 8.6/7.1 => θ = arctan(8.6/7.1) ≈ 50.5° East of South<br /><br /><br />Remember that the graphical method will have some inherent inaccuracy due to the limitations of drawing and measuring. The calculated values are more precise. Always clearly indicate the scale used on your diagram.<br />