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Coplanar

A set of points is set to be coplanar if and only if they lie on the same geometric plane. Three points are always coplanar.

Other points can be shown to be coplanar by determining that the scalar product of a vector normal to the plane and a vector from any point on the plane to the point being tested is 0.

Properties

If three 3-dimensional vectors $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are coplanar, and $\mathbf{a}\cdot\mathbf{b} = 0$ :

$(\mathbf{c}\cdot\mathbf{\hat a})\cdot\mathbf{\hat a}\ +\ (\mathbf{c}\cdot\mathbf{\hat b})\cdot\mathbf{\hat b} \ =\ \mathbf{\hat c}$

Or, the vector resolutes of $\mathbf{c}$ on $\mathbf{a}$ and $\mathbf{c}$ on $\mathbf{b}$ add to give the original $\mathbf{c}$ .

External links

MathWorld's entry on "coplanar"

Categories: Geometry

Last updated: 05-27-2005 19:49:37

Science Fair Project Encyclopedia Contents Page

10-26-2009 08:16:03
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