/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Find an equation of the plane th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 12

Find an equation of the plane that passes through the point \(P_{0}\) with a normal vector \(\mathbf{n}\). $$P_{0}(1,0,-3) ; \mathbf{n}=\langle 1,-1,2\rangle$$

Short Answer

Expert verified
The equation of the plane is x - y + 2z + 5 = 0.

Step by step solution

01

Identify the coefficients of the normal vector

From the given normal vector \(\mathbf{n}=\langle 1,-1,2\rangle\), we can identify the coefficients as \(a=1, b=-1\), and \(c=2\). These coefficients will be used in the equation of the plane.
02

Substitute the point and coefficients into the equation of a plane

We are given the point \(P_{0}(1,0,-3)\). Substitute the coordinates of the point and the coefficients obtained from the normal vector into the equation of the plane: \(ax + by + cz = d\). Therefore we have: \(1(x-1)-(y-0)+2(z+3)=0\)
03

Simplify the equation

Now, let's simplify the equation: \(x-1-y+2z+6=0\) Combining all the terms, we get: \(x-y+2z+5=0\)
04

Write the final answer

Finally, the equation of the plane that passes through the point \(P_{0}(1,0,-3)\) with a normal vector \(\mathbf{n}=\langle 1,-1,2\rangle\) is: $$x-y+2z+5=0$$

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Identify and briefly describe the surfaces defined by the following equations. $$y=4 z^{2}-x^{2}$$

Identify and briefly describe the surfaces defined by the following equations. $$9 x^{2}+y^{2}-4 z^{2}+2 y=0$$

Use the method of your choice to ate the following limits. $$\lim _{(x, y) \rightarrow(2,0)} \frac{1-\cos y}{x y^{2}}$$

Rectangular boxes with a volume of \(10 \mathrm{m}^{3}\) are made of two materials. The material for the top and bottom of the box costs \(\$ 10 / \mathrm{m}^{2}\) and the material for the sides of the box costs \(\$ 1 / \mathrm{m}^{2}\). What are the dimensions of the box that minimize the cost of the box?

Identify and briefly describe the surfaces defined by the following equations. $$x^{2} / 4+y^{2}-2 x-10 y-z^{2}+41=0$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.