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61. Find an equation for the plane consisting of all points that a equidistant from the points (1, 0, −2) and (3, 4, 0).

61. Find an equation for the plane consisting of all points that a equidistant from the points (1, 0, −2) and (3, 4, 0).

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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5, -1) and con- -3t -1, 3) and 1, 4) and contains + 3z = 1 and -2,5) and 2z = 5x + 4y 1) and is perpen- + 3z = 4 ersection of the pendicular to the - 2z = 6 - 3z = 15 5,6) intersect on of the planes x + y + z = 0 58. 3x - 2y + z = 1, rpendicular, ound to one + planes. 59-60 Find symmetric equations for the line of intersection of the 59. 5.x - 2y - 2z = 1, 60. z = 2x - y - 5, z = 4x + 3y - 5 4x + y + z = 6 61. Find an equation for the plane consisting of all points that are equidistant from the points (1, 0, -2) and (3, 4, 0). 62. Find an equation for the plane consisting of all points that are equidistant from the points (2, 5, 5) and (-6, 3, 1). ne given plane. - 2 = 7 y + 2z = 5 66. Find parametric equations for the line through the point 0 (0, 1, 2) that is perpendicular to the line x = 1 + 1, y = 1 -t, z = 2t and intersects this line. 20 63. Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. 64. (a) Find the point at which the given lines intersect: r = (1, 1,0) + t(1, -1, 2) r = (2, 0, 2) + s(-1, 1, 0) (b) Find an equation of the plane that contains these lines. 65. Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane x + y + z = 2 and perpendicular to the line x = 1 + t, y = 1-t, z = 2t. L₁ any 67. Which of the following four planes are parallel? Are a them identical? P₁: 3x + 6y - 3z = 6 P3: 9y = 1 + 3x + 6z P2: 4x - 12y + 8z = 5 P4: z = x + 2y - 2 68. Which of the following four lines are parallel? Are any of them of
Transcribed Image Text:5, -1) and con- -3t -1, 3) and 1, 4) and contains + 3z = 1 and -2,5) and 2z = 5x + 4y 1) and is perpen- + 3z = 4 ersection of the pendicular to the - 2z = 6 - 3z = 15 5,6) intersect on of the planes x + y + z = 0 58. 3x - 2y + z = 1, rpendicular, ound to one + planes. 59-60 Find symmetric equations for the line of intersection of the 59. 5.x - 2y - 2z = 1, 60. z = 2x - y - 5, z = 4x + 3y - 5 4x + y + z = 6 61. Find an equation for the plane consisting of all points that are equidistant from the points (1, 0, -2) and (3, 4, 0). 62. Find an equation for the plane consisting of all points that are equidistant from the points (2, 5, 5) and (-6, 3, 1). ne given plane. - 2 = 7 y + 2z = 5 66. Find parametric equations for the line through the point 0 (0, 1, 2) that is perpendicular to the line x = 1 + 1, y = 1 -t, z = 2t and intersects this line. 20 63. Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. 64. (a) Find the point at which the given lines intersect: r = (1, 1,0) + t(1, -1, 2) r = (2, 0, 2) + s(-1, 1, 0) (b) Find an equation of the plane that contains these lines. 65. Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane x + y + z = 2 and perpendicular to the line x = 1 + t, y = 1-t, z = 2t. L₁ any 67. Which of the following four planes are parallel? Are a them identical? P₁: 3x + 6y - 3z = 6 P3: 9y = 1 + 3x + 6z P2: 4x - 12y + 8z = 5 P4: z = x + 2y - 2 68. Which of the following four lines are parallel? Are any of them of
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