Question

If two lines are perpendicular to the same line, then they are always, sometimes, or never parallel

Answer 1

let
\[\large y=m_1x+b_1 \]
\[\large y=m_2x+b_2 \]
\[\large y=m_3x+b_3 \]
say lines 1 and 2 are both perpendicular to line 3 so
\[\large m_1m_3=m_2m_3=-1 \]
so
\[\large m_1m_3=m_2m_3 \]
then
\[\large m_1=m_2 \]

Answer 2

Sometime, becuz what if they r 3 dimensional

Answer 3

good point, it would depend on the dimension of the space we r working on.