This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To express the vectors graphically, we convert their polar coordinates (magnitude, angle) into Cartesian coordinates (x, y) and then describe how to draw them on a coordinate plane. The angle is measured counter-clockwise from the positive x-axis. The conversion formulas are: x = r y = r Step 1: Convert vector AB to Cartesian coordinates. Given AB = (2 cm, 030^): x_AB = 2 (30^) = 2 × sqrt(3)2 = sqrt(3) cm y_AB = 2 (30^) = 2 × (1)/(2) = 1 cm So, AB = (sqrt(3), 1) cm ≈ (1.73, 1) cm. To draw AB: Start at the origin (0,0). Draw an arrow 2 cm long at an angle of 30^ counter-clockwise from the positive x-axis. Step 2: Convert vector BC to Cartesian coordinates. Given BC = (6 cm, 270^): x_BC = 6 (270^) = 6 × 0 = 0 cm y_BC = 6 (270^) = 6 × (-1) = -6 cm So, BC = (0, -6) cm. To draw BC: Start at the origin (0,0). Draw an arrow 6 cm long pointing directly downwards along the negative y-axis. Step 3: Convert vector CD to Cartesian coordinates. Given CD = (4 cm, 180^): x_CD = 4 (180^) = 4 × (-1) = -4 cm y_CD = 4 (180^) = 4 × 0 = 0 cm So, CD = (-4, 0) cm. To draw CD: Start at the origin (0,0). Draw an arrow 4 cm long pointing directly left along the negative x-axis. Step 4: Describe the graphical representation of the sequence of vectors. To express these vectors graphically as a sequence of displacements: 1. Draw a Cartesian coordinate system. 2. Place the tail of AB at the origin (0,0). Draw an arrow from (0,0) to (sqrt(3), 1). Label the tail A and the head B. 3. Place the tail of BC at point B (sqrt(3), 1). Draw an arrow from B to (sqrt(3)+0, 1-6) = (sqrt(3), -5). Label the head C. 4. Place the tail of CD at point C (sqrt(3), -5). Draw an arrow from C to (sqrt(3)-4, -5+0) = (sqrt(3)-4, -5). Label the head D. The final positions are: Point A: (0,0) Point B: (sqrt(3), 1) Point C: (sqrt(3), -5) Point D: (sqrt(3)-4, -5) The graphical representation involves drawing these arrows on a coordinate plane according to their magnitudes and directions. Send me the next one 📸