Q 62. Prove Theorem 10.40. That is, sh... [FREE SOLUTION]

Chapter 10: Q 62. (page 847)

Prove Theorem 10.40. That is, show that if $P = (x_{0}, y_{0}, z_{0})$ is a point on plane $鈩�$ then the distance between the origin and $鈩�$ is given by $|<x_{0}, y_{0}, z_{0}> 路 n|$ where $n$ is a unit normal vector to $鈩�$

Short Answer

Expert verified

The distance between the origin and the plane $蚁$ is given by $|<x_{0}, y_{0}, z_{0}> 路 n|$ where $n$ is a unit normal vector to the plane $鈩�$

Step by step solution

Given information

The point $P = (x_{0}, y_{0}, z_{0})$ on the plane $鈩�$

Calculation

The goal is to demonstrate that the distance between the origin and the plane is equal $鈩�$ is given by $|<x_{0}, y_{0}, z_{0}> 路 n|$ , where $n$ is a unit normal vector to the plane $蚁 .$

The direction vector of the point $P = (x_{0}, y_{0}, z_{0})$ and the origin $(0, 0, 0)$ is:

$d = <x_{0} - 0, y_{0} - 0, z_{0} - 0> = <x_{0}, y_{0}, z_{0}>$

Calculation

The distance is given by:

Distance = | d 路 n | = |<x_{0}, y_{0}, z_{0}> 路 n|

Therefore, the distance between the origin and the plane $蚁$ is given by $|<x_{0}, y_{0}, z_{0}> 路 n|$ , where $n$ is a unit normal vector to the plane $鈩�$

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91影视

Prove Theorem 10.40. That is, show that if $P = (x_{0}, y_{0}, z_{0})$ is a point on plane $鈩�$ then the distance between the origin and $鈩�$ is given by $|<x_{0}, y_{0}, z_{0}> 路 n|$ where $n$ is a unit normal vector to $鈩�$

Short Answer

Step by step solution

Given information

Calculation

Calculation

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91影视

Prove Theorem 10.40. That is, show that if P=x0,y0,z0is a point on plane鈩�then the distance between the origin and 鈩�is given by x0,y0,z0路nwhere nis a unit normal vector to 鈩�

Short Answer

Step by step solution

Given information

Calculation

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Discrete Mathematics

Calculus

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Prove Theorem 10.40. That is, show that if $P = (x_{0}, y_{0}, z_{0})$ is a point on plane $鈩�$ then the distance between the origin and $鈩�$ is given by $|<x_{0}, y_{0}, z_{0}> 路 n|$ where $n$ is a unit normal vector to $鈩�$