Find an equation of the plane that passes through the point Po(0, -2,3) with a normal vector n = (1,-1, 1).The equation of the plane that passes through the point Po(0, -2,3) with a normal vector n = (1, -1, 1) is(Type an equation.)

To find the equation of a plane that passes through the point with a normal vector , you can use…

Answered: Find an equation of the plane that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Find an equation of the plane that passes through the point Po(0, -2,3) with a normal vector n = (1,-1, 1).
The equation of the plane that passes through the point Po(0, -2,3) with a normal vector n = (1, -1, 1) is
(Type an equation.)

Expert Solution

Step 1: Point-normal form of the equation of a plane

To find the equation of a plane that passes through the point $P subscript 0 not stretchy left parenthesis 0 comma negative 2 comma 3 not stretchy right parenthesis$ with a normal vector $n equals not stretchy left angle bracket 1 comma negative 1 comma 1 not stretchy right angle bracket$ , you can use the point-normal form of the equation of a plane:

$n times not stretchy left parenthesis r minus P subscript 0 not stretchy right parenthesis equals 0$

Where:
- $n$ is the normal vector.
- $r$ is a point on the plane.
- $P subscript 0$ is the given point on the plane $x minus y plus z minus 3 equals 0$