![Find the magnitude of vector a + b, where a = [1, -3] and b = [5, 2].](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1776605308867-24ef67b30d49f970.png&w=3840&q=75)
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
To determine the magnitude of vector a + b, we first need to find the sum of the vectors a and b, and then calculate the magnitude of the resulting vector. Step 1: Identify the given vectors. a = 1 \\ -3 b = 5 \\ 2 Step 2: Calculate the sum of the vectors a + b. To add vectors, we add their corresponding components. a + b = 1 \\ -3 + 5 \\ 2 = 1 + 5 \\ -3 + 2 = 6 \\ -1 Step 3: Calculate the magnitude of the resulting vector a + b. For a vector v = x \\ y , its magnitude ||v|| is given by the formula ||v|| = sqrt(x^2 + y^2). Let v = a + b = 6 \\ -1 . ||a + b|| = sqrt(6^2 + (-1)^2) ||a + b|| = sqrt(36 + 1) ||a + b|| = sqrt(37) Step 4: Compare with the given options. a. sqrt(34) b. 5 c. 2 d. sqrt(37) The calculated magnitude matches option d. The final answer is d. sqrt(37). 3 done, 2 left today. You're making progress.