   Chapter 11, Problem 6PS

Chapter
Section
Textbook Problem

# Orthogonal Vectors Let P 0 be a point in the plane with normal vector n. Describe the set of points P in the plane for which ( n + P P 0 ⇀ ) is orthogonal to ( n − P P 0 ⇀ ) .

To determine
The set of points P in the plane such that (n+PP0) is orthogonal to (nPP0).

Explanation

Consider the diagram given below,

In the diagram given above the plane contains a point P0 with the normal vector n. There is a point P in the plane as shown in the figure above.

Consider the triangle ABD, from the triangle rule of vector addition,

DB=AB+DA

As,

DA=nAB=PP0

Therefore,

DB=n+PP0

Now, consider the triangle ABC and apply the triangle rule of vector addition,

AB=CB+AC

That is,

AC=ABCB

Since,

AB=

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