1. The problem statement, all variables and given/known data Prove that the set of all 3-vectors orthogonal to [1, -1, 4] forms a subspace of R^3. 2. Relevant equations Orthogonal means dot product is 0. 3. The attempt at a solution I know the vectors in this subspace are of the form [a,b,c] where a - b + 4c = 0. However I don't know how to use this to show there is closure under vector addition and scalar multiplication.