Prove that the set of all 3-vectors orthogonal to [1, -1, 4] forms a subspace of R^3.
Orthogonal means dot product is 0.
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.