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
Step 1: Calculate the scalar multiplication of vector A. Given vector A = (3, 5). -2A = -2 × (3, 5) = (-2 × 3, -2 × 5) = (-6, -10) Step 2: Calculate the scalar multiplication of vector B. Given vector B = (4, 6). 3B = 3 × (4, 6) = (3 × 4, 3 × 6) = (12, 18) Step 3: Calculate the vector sum -2A + 3B. Add the corresponding components of the resulting vectors. -2A + 3B = (-6, -10) + (12, 18) = (-6 + 12, -10 + 18) = (6, 8) Step 4: Calculate the magnitude of the resulting vector. The magnitude of a vector (x, y) is given by the formula sqrt(x^2 + y^2). ||-2A + 3B|| = ||(6, 8)|| = sqrt(6^2 + 8^2) ||-2A + 3B|| = sqrt(36 + 64) ||-2A + 3B|| = sqrt(100) ||-2A + 3B|| = 10 The magnitude is 10. 3 done, 2 left today. You're making progress.