1. The problem statement, all variables and given/known data Given vectors a=(1,-1,0,2,1) b=(3,1,-2,-1,0) and c=(1,5,2,4,-4), which are mutually orthogonal, find a system of linear equations that a vector x must satisfy so it is orthogonal to a, b, and c. 2. Relevant equations None I think. 3. The attempt at a solution This is part A of the problem, after which I just have to solve the system and I'm confident I can do the rest once I have it, but I don't know where to start. I tried using the equations: x1-x2+3x4+x5=0 3x1+x2-2x3-x5=0 x1+5x2+2x3+4x4-4x5=0 And then just solving the matrix, which gives me x=(0,0,0,0,0)+s(-8,2,-11,5,0)+t(-5,5,-6,0,2) But I'm pretty sure this doesn't answer the problem. I don't know how to create a system that gives orthogonal solutions, and the above solution isn't even a vector as far as I know. How do I start this problem? Any tips are much appreciated! Thanks.