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 position vectors of points A and B. The position vector of point A is OA = 7i + 3j - k. The position vector of point B is OB = 2i - 5j + 4k. Step 2: 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 - 5j + 4k) - (7i + 3j - k) AB = (2-7)i + (-5-3)j + (4-(-1))k AB = -5i - 8j + 5k Step 3: Calculate the magnitude of vector AB. The magnitude of a vector xi + yj + zk is given by sqrt(x^2 + y^2 + z^2). ||AB|| = sqrt((-5)^2 + (-8)^2 + (5)^2) ||AB|| = sqrt(25 + 64 + 25) ||AB|| = sqrt(114) Step 4: Compare the result with the given options. The calculated magnitude is sqrt(114). This matches option (b). The final answer is (b) sqrt(114). Last free one today — make it count tomorrow, or type /upgrade for unlimited.