# Thornton & Marion, Classical Dynamics of Particles and Systems, 5th Edition

## Chapter 1. Matrices, Vectors, and Vector Calculus

### Problem 08. An equation of a plane in vector form

#### The problem asks you to

- Show that the given equation is the equation of a plane.

#### This problem assumes

- $latex \\vec{A}$ be a vector from the origin to a fixed point $latex P$
- $latex \\vec{r}$ be a vector from the origin to a variabel point $latex Q(x_1,x_2,x_3)$

#### We should know about

- The equation of a plane, which is the form of

#### Solution

Let the vector $latex \\vec{A}$ be

Then,

Thus,

It is the equation of a plane perpendicular to $latex \\vec{A}$ and passing through the point $latex P$.

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