1. The problem statement, all variables and given/known data Consider z = -3x - y + 11 Find a unit vector perpendicular to the plane, and find a vector parallel to the plane. 2. Relevant equations 3. The attempt at a solution 1.) 0 = -3x - y + 11 - z -11 = - 3x - y - z Perpendicular vector is then: -3i -j -k And to make that a unit vector, divide it by sqrt(11) 2.) Here's what I'm not sure of. Can I just pick anything that gives me a dot product of 0 with the above? Such that: - 3a - b - c = 0? Choosing a = -3, b = 5, c = 4, A parallel vector to the plane is -3i + 5j + 4k? Or is that incorrect?