Doing MIT OCW 18.06 using Gilbert Strang Intro to Linear Algebra. Ch 1.2 The vectors that are perpendicular to <1,1,1> and <1,2,3> lie on a ___________. I would have said "plane". I've worked with vectors in calculus, and if you take the cross product of those two vectors you get a vector perpendicular to both, and you could, visualizing it, move that vector around on the surface of the plane defined by <1,1,1> and <1,2,3>... But the answer given in the solution manual is "line"... How are all the vectors perpendicular to <1,1,1> and <1,2,3> lying on a line?