1. The problem statement, all variables and given/known data Let L be the line in R^3 spanned by v1=(1,1,1) Find a basis (v2,v3) for the plane perpendicular to L, and verify that B=(v1,v2,v3) is a basis for R^3. 2. Relevant equations 3. The attempt at a solution I know that if two vectors are perpendicular or orthogonal that their dot product is equal to zero. However, I am not sure how to find a plane that is perpendicular to a vector.