![Add the following vectors: a) X + Y where X = [10, 4] and Y = [-4, 8]; b) [7, 2] + [5, -1]. Find AB as a column vector if OA = [2, 4] and OB = [3, 2].](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1779121838674-9a30d0f7aadb598d.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
b) Step 1: Add the corresponding components of the vectors. X + Y = 10 \\ 4 + -4 \\ 8 = 10+(-4) \\ 4+8 Step 2: Simplify the components. X + Y = 6 \\ 12 The sum is 6 \\ 12 . c) Step 1: Add the corresponding components of the vectors. 7 \\ 2 + 5 \\ -1 = 7+5 \\ 2+(-1) Step 2: Simplify the components. 7 \\ 2 + 5 \\ -1 = 12 \\ 1 The sum is 12 \\ 1 . 2. Find AB as a column vector Given OA = 2 \\ 4 and OB = 3 \\ 2 . Step 1: Use the formula for finding a vector between two points: AB = OB - OA. AB = 3 \\ 2 - 2 \\ 4 Step 2: Subtract the corresponding components. AB = 3-2 \\ 2-4 Step 3: Simplify the components. AB = 1 \\ -2 The column vector AB is 1 \\ -2 . That's 2 down. 3 left today — send the next one.