Find the equation for the plane through the points Po(-1,- 5,-3), Qo (3, − 4, − 1), and Rō(4,4,1).The equation of the plane is

Answered: Find the equation for the plane through…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the equation for the plane through the points Po(-1,- 5,-3), Qo (3, − 4, − 1), and Rō(4,4,1).
The equation of the plane is

Expert Solution

Step 1: Determine the given information:

The given points are $P subscript 0 left parenthesis negative 1 comma negative 5 comma negative 3 right parenthesis comma Q subscript 0 left parenthesis 3 comma negative 4 comma negative 1 right parenthesis comma R subscript 0 left parenthesis 4 comma 4 comma 1 right parenthesis$ .

The aim is to find the equation of the plane which passes through the given points.

The equation of the plane passes through $open parentheses x subscript 1 comma y subscript 1 comma z subscript 1 close parentheses comma open parentheses x subscript 2 comma y subscript 2 comma z subscript 2 close parentheses$ and $open parentheses x subscript 3 comma y subscript 3 comma z subscript 3 close parentheses$ is $open vertical bar table row cell x minus x subscript 1 end cell cell y minus y subscript 1 end cell cell z minus z subscript 1 end cell row cell x subscript 2 minus x subscript 1 end cell cell y subscript 2 minus y subscript 1 end cell cell z subscript 2 minus z subscript 1 end cell row cell x subscript 3 minus x subscript 1 end cell cell y subscript 3 minus y subscript 1 end cell cell z subscript 3 minus z subscript 1 end cell end table close vertical bar equals 0$ .