Mathematics · Ch 6 — Applications of Vector Algebra

Different Forms of Equation of a Plane

6.8

Different Forms of Equation of a Plane

Definition 6.8. A vector perpendicular to a plane is called a normal to the plane.

Note

Every normal to a plane is perpendicular to every straight line lying in that plane.

A plane is uniquely fixed by any ONE of the following pieces of data:

a unit normal to the plane and the plane's (perpendicular) distance from the origin;
a point of the plane and a normal to the plane;
three non-collinear points of the plane;
a point of the plane, together with two non-parallel vectors (or lines) parallel to the plane;
two distinct points of the plane, together with a non-zero vector (or line) parallel to the plane but not parallel to the line joining the two points. …

Figure 6.24Fig. 6.24 — Vector equation of a plane in normal form: $\overrightarrow{OA}=p\hat d$, with unit normal $\hat d$ and a point $P$ on the plane

$Fig. 6.24 — Fig. 6.24 — Vector equation of a plane in normal form: $\overrightarrow{OA}=p\hat d$, with unit normal $\hat d$ and a point $P$ on the plane$

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. Fig. 6.24 — Vector equation of a plane in normal form: $\overrightarrow{OA}=p\hat d$ , with unit normal $\hat d$ and a point $P$ o …

Figure 6.25Fig. 6.25 — Plane through a point $A$ perpendicular to a vector $\vec n$, with an arbitrary point $P$ on the plane

$Fig. 6.25 — Fig. 6.25 — Plane through a point $A$ perpendicular to a vector $\vec n$, with an arbitrary point $P$ on the plane$

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. Fig. 6.25 — Plane through a point $A$ perpendicular to a vector $\vec n$ , with an arbitrary point $P$ on th …

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