Question: how to find the equation of a plane perpendicular to a vector?
Answer: Namely, ⟨a,b,c⟩ is perpendicular to the vector with tail at (d/a,0,0) and head at (x,y,z). This means that the points (x,y,z) that satisfy the equation ax+by+cz=d form a plane perpendicular to ⟨a,b,c⟩.