Chapter 13

The plane through 2 1 0 and parallel to x 19 the

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Unformatted text preview: the surface whose equation is given. 40. 1 t, 2 t. 1 1 y 2 x 2 z 3 1 6 y 3 3 1 z 5 2 are parallel, skew, or intersecting. 24. (a) Show that the planes x 42. r y z 1 and 2 x 3y 4z 5 are neither parallel nor perpendicular. (b) Find, correct to the nearest degree, the angle between these planes. 4 43. cos ■ ■ ■ ■ ■ ■ 3 sec ■ ■ ■ ■ ■ 44–46 |||| Write the equation in cylindrical coordinates and in spherical coordinates. 44. x 2 4 41. 4 ■ equations x 1 . Find the cylindrical and spherical coordinates of the point. 23. Determine whether the lines given by the symmetric and 4z 2y ■ 0 39. The spherical coordinates of a point are 8, ■ 22. Find the distance from the origin to the line x 2 2 38. The rectangular coordinates of a point are 2, 2, 2 that contains the line x 21. Find the point in which the line with parametric equations y z z2 8y 3, 2). Find the rectangular and spherical coordinates of the point. 3t ■ x 2 t, y 2x y z x 4 2 37. The cylindrical coordinates of a point are (2 s3, 1 1, 1 , 4, 0, 2 , and 6, 3, 1 20. The plane through 1, 2, 3 2 4z 2 36. A surface consists of all points P such that the distance from ■ Find an equation of the plane. ■ 1 4y ■ 4z 2 2 y2 4 2 2 z 2 about the x-axis. Find an equation of the ellipsoid. 12 ■ 19. The plane through 3, y 2 35. An ellipsoid is created by rotating the ellipse 4 x 2 2, 2, 4 and perpendicular to the plane 18. The plane through 2, 1, 0 and parallel to x ■ 2 y ■ y z 34. x 2z 2 2 33. 4 x 29. x y 4x 32. y Find parametric equations for the line. 15. The line through 4, 2 30. 4 x 40 cm 27. x 3 28. y 4z y 24. Identify and sketch the graph of each surface. |||| 26. x 4z y y2 2 2 46. x ■ y ■ 45. x 2 4 z ■ 2 y2 z2 4 2x ■ ■ ■ ■ ■ ■ ■ ■ 4 y 2, x 0 is rotated about the z -axis. Write an equation of the resulting surface in cylindrical coordinates. 47. The parabola z 48. Sketch the solid consisting of all points with spherical coordi- nates 0 such that 0 ,, 2 cos . 2, 0 6, and ■ 5E-13(pp 878-883) 1/18/06 1...
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas.

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