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Mathematics · Glossary

What is Plane?

Definition 31.4 High School Mathematics · Chapter 31 — Vectors, Lines and Planes in Space

The plane through $A$ directed by two non-collinear vectors $\vec u, \vec v$ is the set of points $M$ with $\vect{AM} = s\vec u + t\vec v$ , $(s, t) \in \R^2$ .

Left: the line through A with direction u, graduated by the parameter t. Right: the plane through A directed by u and v; every point M of the plane is reached as AM = s u + t v. — Left: the line through $A$ with direction $\vec u$ , graduated by the parameter $t$ . Right: the plane through $A$ directed by $\vec u$ and $\vec v$ ; every point $M$ of the plane is reached as $\vect{AM} = s\vec u + t\vec v$ .

Left: the line through A with direction u, graduated by the parameter t. Right: the plane through A directed by u and v; every point M of the plane is reached as AM = s u + t v. — Left: the line through $A$ with direction $\vec u$ , graduated by the parameter $t$ . Right: the plane through $A$ directed by $\vec u$ and $\vec v$ ; every point $M$ of the plane is reached as $\vect{AM} = s\vec u + t\vec v$ .

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