Find the equation for the plane through the points Po(-1, −5, − 3), Q₁ (3, — 4, − 1), and Rō(4,4,1 The equation of the plane is

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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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
Transcribed Image Text: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.

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