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41-44 Use intercepts to help sketch the plane. 41. 2x + 5y + z = 10 43. 6.x - 3y + 4z = 6 42. 3x + y + 2z = 6 44. 6x + 5y - 3z = 15

41-44 Use intercepts to help sketch the plane. 41. 2x + 5y + z = 10 43. 6.x - 3y + 4z = 6 42. 3x + y + 2z = 6 44. 6x + 5y - 3z = 15

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question

43

37. The plane that passes through the point (3, 1, 4) and co the line of intersection of the planes x + 2y + 3z = 1 and 2x = y + z = -3 38. The plane that passes through the points (0, -2, 5) and (-1, 3, 1) and is perpendicular to the plane 2z = 5x + 4y 39. The plane that passes through the point (1, 5, 1) and is perpen- dicular to the planes 2x + y - 2z = 2 and x + 3z = 4 40. The plane that passes through the line of intersection of the = 1 and y + 2z = 3 and is perpendicular to the planes x -z = plane x + y - 2z = 1 41-44 Use intercepts to help sketch the plane. 41. 2x + 5y + z = 10 43. 6x - 3y + 4z = 6 42. 3x + y + 2z = 6 44. 6x + 5y - 3z = 15 45-47 Find the point at which the line intersects the given plane. 45. x = 2 - 2t, y = 3t, z = 1+ t; x+2y=z=785 46. x = t - 1, y = 1 + 2t, z = 3 = t; 3x-y + 2z = 5 47. 5x = y/2 = z + 2; 10x - 7y + 3z + 24 = 0 the plane 2x + y = z = -2? 48. Where does the line through (-3, 1, 0) and (-1, 5, 6) intersect x + y + z = 1 and x + z = 0. 49. Find direction numbers for the line of intersection of the planes and x + 2y + 3z = 1. 50. Find the cosine of the angle between the planes x+y+z=0 decimal place.) 51-56 Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one 51. x + 4y - 3z = 1, 52. 9x - 3y + 6z = 2, 53. x + 2y - z = 2, 54. x - y + 3z = 1, 55. 2x - 3y = z, 56. 5x + 2y + 3z = 2, y = 4 -3x + 6y + 7z = 0 2y = 6x + 4z 2x - 2y + z = 1 3x + y -z=2 4x = 3 + 6y + 2z 59. 5x - 2y 60. z = 2x - 61. Find an eq equidistan 62. Find an eq equidistant 63. Find an eq and z-inter 64. (a) Find th (b) Find an 65. Find param (0, 1, 2) thar perpendicul 66. Find parame (0, 1, 2) that y=1-1, z 67. Which of the them identica P₁: 3x P3: 9y 68. Which of the identical? L₁: x = L₂: x = L3: 2x L₁: r = 69-70 Use the form from the point to th
Transcribed Image Text:37. The plane that passes through the point (3, 1, 4) and co the line of intersection of the planes x + 2y + 3z = 1 and 2x = y + z = -3 38. The plane that passes through the points (0, -2, 5) and (-1, 3, 1) and is perpendicular to the plane 2z = 5x + 4y 39. The plane that passes through the point (1, 5, 1) and is perpen- dicular to the planes 2x + y - 2z = 2 and x + 3z = 4 40. The plane that passes through the line of intersection of the = 1 and y + 2z = 3 and is perpendicular to the planes x -z = plane x + y - 2z = 1 41-44 Use intercepts to help sketch the plane. 41. 2x + 5y + z = 10 43. 6x - 3y + 4z = 6 42. 3x + y + 2z = 6 44. 6x + 5y - 3z = 15 45-47 Find the point at which the line intersects the given plane. 45. x = 2 - 2t, y = 3t, z = 1+ t; x+2y=z=785 46. x = t - 1, y = 1 + 2t, z = 3 = t; 3x-y + 2z = 5 47. 5x = y/2 = z + 2; 10x - 7y + 3z + 24 = 0 the plane 2x + y = z = -2? 48. Where does the line through (-3, 1, 0) and (-1, 5, 6) intersect x + y + z = 1 and x + z = 0. 49. Find direction numbers for the line of intersection of the planes and x + 2y + 3z = 1. 50. Find the cosine of the angle between the planes x+y+z=0 decimal place.) 51-56 Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one 51. x + 4y - 3z = 1, 52. 9x - 3y + 6z = 2, 53. x + 2y - z = 2, 54. x - y + 3z = 1, 55. 2x - 3y = z, 56. 5x + 2y + 3z = 2, y = 4 -3x + 6y + 7z = 0 2y = 6x + 4z 2x - 2y + z = 1 3x + y -z=2 4x = 3 + 6y + 2z 59. 5x - 2y 60. z = 2x - 61. Find an eq equidistan 62. Find an eq equidistant 63. Find an eq and z-inter 64. (a) Find th (b) Find an 65. Find param (0, 1, 2) thar perpendicul 66. Find parame (0, 1, 2) that y=1-1, z 67. Which of the them identica P₁: 3x P3: 9y 68. Which of the identical? L₁: x = L₂: x = L3: 2x L₁: r = 69-70 Use the form from the point to th
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