Take for example a diagonal line $L$ that lies in $y=0$ (in a cube, with equation $x = t$, $z = -x = -t, y = 0$), that line is perpendicular to line $x = t, z = x = t,y = 0$, and then surprisingsly also perpendicular with space diagonal line with equation $x = t , y = t, z = t$ (surprising if you didn't use vector and use cosine rule instead), and it's also perpendicular to the normal line of $y = 0$ (that is the line $y = t, x = 0, z = 0 $).
My Question :
1) Just how many possible sets of lines are perpendicular to $L$ ? does those set of lines as segment form some kind of circle around that particular line ?
2)What rotation doesn't change the perpendicularity of two lines ?
Two lines in $\mathbb{R}^3$ are perpendicular iff:
The set of lines that are perpendicular to a given line form a series of planes, whose normals are parallel to the given line.