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Calculus / Calculus: Early Transcendentals 1 / Chapter 12.1 / Problem 4E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Give an equation of the plane with a normal vector n = ?1,

Chapter 12, Problem 4E

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QUESTION:

What is an equation of the plane with a normal vector \(\mathbf{n}=\langle 1,1,1\rangle\) that passes through the point (1,0,0)?

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QUESTION:

What is an equation of the plane with a normal vector \(\mathbf{n}=\langle 1,1,1\rangle\) that passes through the point (1,0,0)?

ANSWER:

Solution 4E

Step 1 of 2:

In this problem we need to find the equation of the plane with a normal vector $n\ =\ 〈1,\ 1,\ 1〉$ that passes through the point (1, 0, 0).

The plane passing through the point ${P}_{0}({x}_{0},{y}_{0},{z}_{0})$ with a nonzero normal vector $n=〈a,b,c〉$

is described by the equation

$a(x-{x}_{0})+b(y-{y}_{0})+c(z-{z}_{0})=0$ .

To find: the equation of the plane with a normal vector $n\ =\ 〈1,\ 1,\ 1〉$ that passes through the point ${P}_{0}$ (1, 0, 0).

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