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In Exercises 3-6, give any two points in the given plane. 3. 2x - 4y +7z=2

In Exercises 3-6, give any two points in the given plane. 3. 2x - 4y +7z=2

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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10.6) question 3
4 2. What is the relationship between a plane and one of its nor- mal vectors? Problems In Exercises 3-6, give any two points in the given plane. 3. 2x - 4y+7z = 2 4. 3(x+2)+5(y-9) - 4z=0 5. x = 2 6. 4(y + 2)-(z - 6) = 0 In Exercises 7-20, give the equation of the described plane in standard and general forms. 7. Passes through (2,3,4) and has normal vector n = (3,-1,7). 8. Passes through (1, 3, 5) and has normal vector n = (0,2,4). 9. Passes through the points (1, 2, 3), (3, -1, 4) and (1, 0, 1). 10. Passes through the points (5, 3, 8), (6, 4, 9) and (3,3,3). 11. Contains the intersecting lines (t) = (2, 1, 2) + t (1, 2, 3) and 2 (t) = (2, 1, 2) + t (2, 5, 4). 12. Contains the intersecting lines O Search I 17. Con e(t) 18. Cont l(t) 19. Conta 3(x- 20. Contai x = 5. In Exercise intersectio 21. p1: 3(x p2: 2(x 22. p1: 5(x p2: 3x- In Exercises. the line and 23. line: (5, 1, plane: 5x - 24. line: (4, 1, C plane: 3x + 25. line: (1, 2, 3, plane: 3x-
Transcribed Image Text:4 2. What is the relationship between a plane and one of its nor- mal vectors? Problems In Exercises 3-6, give any two points in the given plane. 3. 2x - 4y+7z = 2 4. 3(x+2)+5(y-9) - 4z=0 5. x = 2 6. 4(y + 2)-(z - 6) = 0 In Exercises 7-20, give the equation of the described plane in standard and general forms. 7. Passes through (2,3,4) and has normal vector n = (3,-1,7). 8. Passes through (1, 3, 5) and has normal vector n = (0,2,4). 9. Passes through the points (1, 2, 3), (3, -1, 4) and (1, 0, 1). 10. Passes through the points (5, 3, 8), (6, 4, 9) and (3,3,3). 11. Contains the intersecting lines (t) = (2, 1, 2) + t (1, 2, 3) and 2 (t) = (2, 1, 2) + t (2, 5, 4). 12. Contains the intersecting lines O Search I 17. Con e(t) 18. Cont l(t) 19. Conta 3(x- 20. Contai x = 5. In Exercise intersectio 21. p1: 3(x p2: 2(x 22. p1: 5(x p2: 3x- In Exercises. the line and 23. line: (5, 1, plane: 5x - 24. line: (4, 1, C plane: 3x + 25. line: (1, 2, 3, plane: 3x-
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