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67. Which of the following four planes are parallel? Are them identical? P₁: 3x + 6y - 3z = 6 P3: 9y = 1 + 3x + 6z any of P2: 4x 12y + 8z = 5 P₁: z = x + 2y - 2

67. Which of the following four planes are parallel? Are them identical? P₁: 3x + 6y - 3z = 6 P3: 9y = 1 + 3x + 6z any of P2: 4x 12y + 8z = 5 P₁: z = x + 2y - 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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on of the ular to the 6 15 plane. = 5 persect anes and z-intercept 64. (a) Find the point at which the given lines intersect: 63. 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. - Juns ont in 66. Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1-t, z = 2t and intersects this line. 67. Which of the following four planes are parallel? Are any of them identical? P₁: 3x+6y3z = 6 P3: 9y = 1 + 3x + 6z P₂: 4x 12y + 8z = 5 P4: z = x + 2y - 2 = 0 identical? 68. Which of the following four lines are parallel? Are any of them L₁: x= 1 + 6t, y = 1 - 3t, - z = 12t + 5 L₂: x= 1 + 2t, yt, z = 1+ 4t L3: 2x2=4 - 4y = z + 1 L4: r = (3, 1,5) + t(4, 2,8) 69-70 Use the formula in Exercise 12.4.45 to find the distance from the point to the given line. poredy 69. (4, 1,-2); x = 1+t, y = 3 - 2t, z = 4 - 3t 70. (0, 1,3); x = 2t,
Transcribed Image Text:on of the ular to the 6 15 plane. = 5 persect anes and z-intercept 64. (a) Find the point at which the given lines intersect: 63. 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. - Juns ont in 66. Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1-t, z = 2t and intersects this line. 67. Which of the following four planes are parallel? Are any of them identical? P₁: 3x+6y3z = 6 P3: 9y = 1 + 3x + 6z P₂: 4x 12y + 8z = 5 P4: z = x + 2y - 2 = 0 identical? 68. Which of the following four lines are parallel? Are any of them L₁: x= 1 + 6t, y = 1 - 3t, - z = 12t + 5 L₂: x= 1 + 2t, yt, z = 1+ 4t L3: 2x2=4 - 4y = z + 1 L4: r = (3, 1,5) + t(4, 2,8) 69-70 Use the formula in Exercise 12.4.45 to find the distance from the point to the given line. poredy 69. (4, 1,-2); x = 1+t, y = 3 - 2t, z = 4 - 3t 70. (0, 1,3); x = 2t,
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