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: Identify the coordinates of points A and B. Point A is (1, 2, 0). Point B is (2, -1, 3). Step 2: Express the position vectors of points A and B. The position vector of A is OA = 1i + 2j + 0k. The position vector of B is OB = 2i - 1j + 3k. Step 3: Calculate the vector AB. The vector AB is found by subtracting the position vector of A from the position vector of B: AB = OB - OA AB = (2i - j + 3k) - (i + 2j + 0k) AB = (2-1)i + (-1-2)j + (3-0)k AB = 1i - 3j + 3k AB = i - 3j + 3k Step 4: Compare the result with the given options. The calculated vector AB = i - 3j + 3k matches option (c). The final answer is (c) i - 3j + 3k. 3 done, 2 left today. You're making progress.