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
Welcome back — been a while! Let's pick up where you left off. a) To find PQ in terms of a, we use the formula PQ = OQ - OP. Step 1: Substitute the given vectors. PQ = (2ai + 5j) - ((a+2)i + j) Step 2: Group the i and j components. PQ = (2a - (a+2))i + (5 - 1)j Step 3: Simplify the expression. PQ = (2a - a - 2)i + 4j PQ = (a - 2)i + 4j The vector PQ in terms of a is (a - 2)i + 4j. b) Given that PQ = 3i + 4j, we equate this to the expression found in part (a). Step 1: Equate the i components. a - 2 = 3 Step 2: Solve for a. a = 3 + 2 a = 5 The value of a is 5. c) To find |PQ|, we use the given vector PQ = 3i + 4j from part (b). The magnitude of a vector xi + yj is given by sqrt(x^2 + y^2). Step 1: Substitute the components of PQ. |PQ| = sqrt(3^2 + 4^2) Step 2: Calculate the squares. |PQ| = sqrt(9 + 16) Step 3: Add the values. |PQ| = sqrt(25) Step 4: Find the square root. |PQ| = 5 The magnitude of PQ is 5. Send me the next one 📸