The line through the point 4 the line through the

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Unformatted text preview: parallel to the line x y t, z 1 4 2t, 3t 5. The line through the point (1, 0, 6) and perpendicular to the plane x ■ ■ z 3y ■ ■ 5 ■ ■ ■ ■ ■ ■ ■ ■ 5E-13(pp 858-867) ❙❙❙❙ 866 6 –12 1/18/06 11:32 AM Page 866 CHAPTER 13 VECTORS AND THE GEOMETRY OF SPACE |||| Find parametric equations and symmetric equations for the line. 23–38 23. The plane through the point 6, 3, 2 and perpendicular to the 7. The line through the points 1, 3, 2 and 8. The line through the points 6, 1, 24. The plane through the point 4, 0, 4, 3, 0 vector j 3 and 2, 4, 5 9. The line through the points (0, , 1) and 2, 1, 1 2 i x 1 2 2 z y the line x ■ 2x 3 z y 1 ■ ■ ■ ■ ■ 4, 6, 1 and 2, 0 line through 10, 18, 4 and 5, 3, 14 ? ■ ■ ■ 3 parallel to the 33. The plane through the points 3, 1, L 2: ■ ■ y 1 2 s, s, y 4 y 1, 4 t, z 1 2 t 2 t, y 4 5 t, z 3 7 the line of intersection of the planes x 2 x y 3z 1 2 and contains 4t 37. The plane that passes through the point 2 2 3 1 2 , z x 3 y 4 z 2 y 1, 1 and 2 y 3z 1, 2, 1 and contains z 2 and 3 3 2 ■ t, y 1 2 t, y ■ ■ ■ ■ ■ y ■ 1 ■ t, z 2 5t ; 4 t, z 2 2z ; 4x ■ y ■ x 3t ; 3z ■ ■ y ■ x 2z ■ ■ the plane x y z 9 z 2y 1 0 8 ■ ■ 42. Where does the line through 1, 0, 1 and 4, ■ ■ ■ 2, 2 intersect 6? 43. Find direction numbers for the line of intersection of the planes x y z 1 and x z 0. 44. Find the cosine of the angle between the planes x 3 ■ ■ 3 and is perpendicular to the Find the point at which the line intersects the given plane. |||| 41. x 1 2 ■ ■ 40. x 3s 2 1 1 ■ L 2: 6 y 1 1 z 2 2 z ■ 2z 1 and y 2z 1 39. x t s, z y planes x plane x 39–41 s 2 3 y z z 4 z 3t 3s, 3 t, y 1 z 9 t, y 2 t, 1 ■ 4, 6 38. The plane that passes through the line of intersection of the 6 t, x 3 t, y contains the line with symmetric equations x ■ 22. L 1: t 1, 2 , 8, 2, 4 , and 36. The plane that passes through the point 1, Determine whether the lines L 1 and L 2 are parallel, skew, or intersec...
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