Perpendicular

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Two lines $l$ and $m$ are said to be perpendicular if they intersect in right angles. We denote this relationship by $l \perp m$. In the Cartesian coordinate system, a line with slope $m$ is perpendicular to every line with slope $-\frac{1}{m}$ and no others.


One can also discuss perpendicularity of other objects. If a line $l$ intersects a plane $P$ at a point $A$, we say that $l \perp P$ if and only if for every line $m$ in $P$ passing through $A$, $l \perp m$.

If a plane $P$ intersects another plane $Q$ in a line $k$, we say that $P \perp Q$ if and only if: for line $l \in P$ and $m \in Q$ passing through $A \in k$, $l \perp k$ and $m \perp k$ implies $l \perp m$.

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