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 your vector problem: i) Find b. Step 1: Substitute the given vectors into the equation a + 2b = c. 2 \\ 3 + 2b = 3 \\ 5 Step 2: Isolate 2b by subtracting vector a from both sides. 2b = 3 \\ 5 - 2 \\ 3 Step 3: Perform the vector subtraction. 2b = 3 - 2 \\ 5 - 3 2b = 1 \\ 2 Step 4: Solve for b by dividing each component by 2. b = (1)/(2) 1 \\ 2 b = (1)/(2) \\ (2)/(2) b = 0.5 \\ 1 The vector b is 0.5 \\ 1 . ii) Find the magnitude of (a + b) correct to 2 decimal places. Step 1: Calculate the vector a + b. a + b = 2 \\ 3 + 0.5 \\ 1 a + b = 2 + 0.5 \\ 3 + 1 a + b = 2.5 \\ 4 Step 2: Calculate the magnitude of a + b. The magnitude of a vector x \\ y is sqrt(x^2 + y^2). |a + b| = sqrt((2.5)^2 + (4)^2) |a + b| = sqrt(6.25 + 16) |a + b| = sqrt(22.25) Step 3: Calculate the square root and round to 2 decimal places. |a + b| ≈ 4.7170 Rounding to 2 decimal places: |a + b| ≈ 4.72 The magnitude of (a + b) is 4.72. Last free one today — make it count tomorrow, or type /upgrade for unlimited.