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'condition of orthogonality'
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| Title of object: |
condition of orthogonality |
| Canonical Name: |
ConditionOfOrthogonality |
| Type: |
Result |
| Created on: |
2004-11-07 10:06:03 |
| Modified on: |
2005-02-19 12:28:08 |
| Classification: |
msc:15A57, msc:51F20 |
| Keywords: |
straight line, slope |
| Defines: |
opposite inverse |
| Synonyms: |
condition of orthogonality=condition of perpendicularity |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx} |
Content:
Let two straight lines of the $xy$-plane have the slopes $m_1$ and $m_2$. \,The lines are at right angles to each other iff $m_1$ and $m_2$ are the {\em opposite inverses} of each other, i.e. \PMlinkname{iff}{Biconditional}
\[m_1m_2 = -1.\]
\textbf{Example.} \,The lines \,$y = (1+\sqrt{2})x$\, and \,$y = (1-\sqrt{2})x$\, are at right angles to each other.
\begin{center}
\includegraphics{orthogon}
\end{center} |
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