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
Given the vectors: A = 3i + 4j + 2k B = 2i - j + 5k Step 1: Calculate the dot product A · B. The dot product is calculated by multiplying corresponding components and summing the results. A · B = (3)(2) + (4)(-1) + (2)(5) A · B = 6 - 4 + 10 A · B = 2 + 10 A · B = 12 Step 2: Calculate the cross product A × B. The cross product can be calculated using the determinant of a matrix: A × B = i & j & k \\ 3 & 4 & 2 \\ 2 & -1 & 5 A × B = i((4)(5) - (2)(-1)) - j((3)(5) - (2)(2)) + k((3)(-1) - (4)(2)) A × B = i(20 - (-2)) - j(15 - 4) + k(-3 - 8) A × B = i(20 + 2) - j(11) + k(-11) A × B = 22i - 11j - 11k What's next? Send 'em! 📸