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37. The plane that passes through the point (3, 1, 4) and contains the line of intersection of the planes x + 2y + 3z = 1 and 2x = y + z = -3

37. The plane that passes through the point (3, 1, 4) and contains the line of intersection of the planes x + 2y + 3z = 1 and 2x = y + z = -3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
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832 CHAPTER 12 Vectors and the Geometry of Space 34. The plane through the points (3, 0, -1), (-2, -2, 3), and (7, 1, −4) 35. The plane that passes through the point (3, 5, -1) and con- tains the line x = 4t, y = 2t - 1, z = -3t 36. The plane that passes through the point (6,-1, 3) and contains the line with symmetric equations x/3 = y + 4 = z/2 37. The plane that passes through the point (3, 1, 4) and contains 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 05 1 40. The plane that passes through the line of intersection of the plane x + y - 2z = 1 planes x -z = 1 and y + 2z = 3 and is perpendicular to the 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 - 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 = 7 3z = 15 46. x = 1 - 1, y = 1 + 2t, z = 3-t; 47. 5x=y/2z+ 2; 10x - 7y + 3z + 24 = 0 3x-y + 2z = 5 GUTE 13 the plane 2x + y -z = -2? 48. Where does the line through (-3, 1, 0) and (-1, 5, 6) intersent 57-58 (a) the planes 57. x + y 58. 3x - 2 59-60 Fin planes. 59. 5x2 60. z = 2x 61. Find an equidis 62. Find an equidist 63. Find an and z-in 64. (a) Finc 201 (b) Find 65. Find para (0, 1, 2) m perpendi 67. 66. Find para (0, 1, 2) t y = 1 -
Transcribed Image Text:832 CHAPTER 12 Vectors and the Geometry of Space 34. The plane through the points (3, 0, -1), (-2, -2, 3), and (7, 1, −4) 35. The plane that passes through the point (3, 5, -1) and con- tains the line x = 4t, y = 2t - 1, z = -3t 36. The plane that passes through the point (6,-1, 3) and contains the line with symmetric equations x/3 = y + 4 = z/2 37. The plane that passes through the point (3, 1, 4) and contains 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 05 1 40. The plane that passes through the line of intersection of the plane x + y - 2z = 1 planes x -z = 1 and y + 2z = 3 and is perpendicular to the 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 - 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 = 7 3z = 15 46. x = 1 - 1, y = 1 + 2t, z = 3-t; 47. 5x=y/2z+ 2; 10x - 7y + 3z + 24 = 0 3x-y + 2z = 5 GUTE 13 the plane 2x + y -z = -2? 48. Where does the line through (-3, 1, 0) and (-1, 5, 6) intersent 57-58 (a) the planes 57. x + y 58. 3x - 2 59-60 Fin planes. 59. 5x2 60. z = 2x 61. Find an equidis 62. Find an equidist 63. Find an and z-in 64. (a) Finc 201 (b) Find 65. Find para (0, 1, 2) m perpendi 67. 66. Find para (0, 1, 2) t y = 1 -
Expert Solution
Step 1

37. The given data is:

The equation of planes are:

x+2y+3z=1            .......12x-y+z=-3        ........2

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