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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