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: Find the vector RS. Given points R(2, 2) and S(5, 4). The vector RS is found by subtracting the coordinates of R from the coordinates of S. RS = S - R = (5-2, 4-2) = (3, 2) Step 2: Calculate the magnitude of RS (part i). The magnitude of a vector (x, y) is given by the formula sqrt(x^2 + y^2). Here, x=3 and y=2. |RS| = sqrt(3^2 + 2^2) |RS| = sqrt(9 + 4) |RS| = sqrt(13) The magnitude k is sqrt(13). Step 3: Calculate the bearing (part ii). The vector RS = (3, 2) is in the first quadrant. Let be the angle the vector makes with the positive x-axis (East). = vertical componenthorizontal component = (2)/(3) = ((2)/(3)) ≈ 33.69^ Bearing is measured clockwise from the North direction (positive y-axis). Since the vector is in the first quadrant, the bearing is 90^ - . = 90^ - 33.69^ = 56.31^ Rounding to one decimal place, ≈ 56.3^. As a 3-digit bearing, this is 056.3^. Step 4: Express RS in the form (k, ). From Step 2, k = sqrt(13). From Step 3, ≈ 056.3^. i) The magnitude of RS is sqrt(13). ii) Express RS in the form (k, ): (sqrt(13), 056.3^).