1. The problem statement, all variables and given/known data Determine a vector that is orthogonal to both (1,2,-1) and (3,1,0) 2. Relevant equations As above. 3. The attempt at a solution The solution, from the back of the book, is "any vector of the form (a, -3a, -5a), but I'm not sure how they got there. I get the methodology for a matrix in two dimensions, like so: Find a matrix orthogonal to (5,1) (5a) + (-b) = 0 5a = b The answer is (a, 5a) or any vector of the form a(1,3) ...but I don't understand how to go about this for the question originally stated.