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 are the solutions to the problems. a) To express the vector PQ as a column vector, subtract the coordinates of point P from the coordinates of point Q. Given P = (2, 4) and Q = (-3, 1). Step 1: Calculate the change in the x-coordinate. x_Q - x_P = -3 - 2 = -5 Step 2: Calculate the change in the y-coordinate. y_Q - y_P = 1 - 4 = -3 Step 3: Write the vector PQ as a column vector. PQ = -5 \\ -3 The vector PQ is -5 \\ -3 . b) Given the vector PQ = -3 \\ 2 and point P = (1, 4). Let the coordinates of point Q be (x, y). Step 1: Set up the vector equation. The vector PQ is found by subtracting the coordinates of P from Q: PQ = x - x_P \\ y - y_P = x - 1 \\ y - 4 We are given PQ = -3 \\ 2 . So, we have the equation: x - 1 \\ y - 4 = -3 \\ 2 Step 2: Solve for the x-coordinate of Q. x - 1 = -3 x = -3 + 1 x = -2 Step 3: Solve for the y-coordinate of Q. y - 4 = 2 y = 2 + 4 y = 6 Step 4: State the coordinates of point Q. The coordinates of point Q are (-2, 6). Send me the next one 📸