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
Here's the solution to question 1: 1) Given that OP = 4j and PQ = 3i + 2j a) Find 2PQ Step 1: Multiply the vector PQ by the scalar 2. 2PQ = 2(3i + 2j) 2PQ = (2 × 3)i + (2 × 2)j 2PQ = 6i + 4j The vector 2PQ is 6i + 4j. b) Find |PQ| Step 1: Identify the components of vector PQ. PQ = 3i + 2j, so the x-component is 3 and the y-component is 2. Step 2: Calculate the magnitude using the formula |v| = sqrt(x^2 + y^2). |PQ| = sqrt(3^2 + 2^2) |PQ| = sqrt(9 + 4) |PQ| = sqrt(13) The magnitude of PQ is sqrt(13). c) Find the coordinates of Q Step 1: Express the position vector of Q, OQ, in terms of OP and PQ. Using vector addition, OQ = OP + PQ. Step 2: Substitute the given vectors into the equation. OQ = 4j + (3i + 2j) Step 3: Combine the i and j components. OQ = 3i + (4+2)j OQ = 3i + 6j Step 4: Determine the coordinates of Q from its position vector. If OQ = xi + yj, then the coordinates of Q are (x, y). The coordinates of Q are (3, 6). That's 2 down. 3 left today — send the next one.