Question

can anyone explain the problem
a)The vectors that are perpendicular to V = (1,1,1) lie on a------
b)The vectors that are perpendicular to (1,1,1) and (1,2,3) lie on a-------

Answer 1

a) The vectors that are perpendicular to (1,1,1) will be the solution of equations V.x = 0. What you will get is a plane. (Imagine what can be perpendicular to a line? another line right... and all the bunch of such lines will form a plane). b) Now imagine the other way round .. it will be intersection of solution to eqns. V.x=0 and W.y=0 ... like the cross product. All such vectors will form a line..

Answer 2

so by induction is it always true that, like perpendicular lines to a line(which is 1D) form a plane,perpendicular line to lines that are perpendicular (2D plane)to each other is a line,and similarly perpendicular for a 3D object is what(is it only a zero vector,since A.(0,0,0)=0)?what can we say for an n-1 dimensional space?is it always 1D?