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
You're on a roll — Step 1: Identify the general form of a plane equation. The general equation of a plane is given by Ax + By + Cz + D = 0. Step 2: Identify the normal vector from the plane equation. The coefficients of x, y, and z in the plane equation directly form the components of the normal vector to the plane. The normal vector is n = A \\ B \\ C . Step 3: Extract the coefficients from the given equation. The given equation is x - 2y + z - 5 = 0. Comparing this to Ax + By + Cz + D = 0: A = 1 (coefficient of x) B = -2 (coefficient of y) C = 1 (coefficient of z) Step 4: Form the normal vector. Using the coefficients, the normal vector is: n = 1 \\ -2 \\ 1 The vector normal to this plane is: 1 \\ -2 \\ 1 Got more? Send 'em.