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26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1,-1, 10), and C(1, 3, -4). (b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a). (c) A second plane passes through (2, 0, 4) and has normal vector (2, -4,-3). Show that the acute angle between the planes is approximately 43°.

26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1,-1, 10), and C(1, 3, -4). (b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a). (c) A second plane passes through (2, 0, 4) and has normal vector (2, -4,-3). Show that the acute angle between the planes is approximately 43°.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1, -1, 10), and C(1, 3, -4). (b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a). (c) A second plane passes through (2, 0, 4) and has normal vector (2, -4, -3). Show that the acute angle between the planes is approximately 43°. (d) Find parametric equations for the line of intersection of the two planes. 27. Find the distance between the planes 3x + y - 4z = 2 and 3x + y - 4z = 24.
Transcribed Image Text:26. (a) Find an equation of the plane that passes through the points A(2, 1, 1), B(-1, -1, 10), and C(1, 3, -4). (b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a). (c) A second plane passes through (2, 0, 4) and has normal vector (2, -4, -3). Show that the acute angle between the planes is approximately 43°. (d) Find parametric equations for the line of intersection of the two planes. 27. Find the distance between the planes 3x + y - 4z = 2 and 3x + y - 4z = 24.
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