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Unformatted text preview: ting. If they intersect, ﬁnd the point of intersection. x 8 3 the line x 3. x
1 2 t, y t, z
17 35. The plane that passes through the point 6, 0,  21. L 1: 2, the line x 18. Find parametric equations for the line segment from 10, 3, 1 L 2: x 8z 34. The plane that passes through the point 1, 2, 3 and contains to 4, 6, 1 . 1 3 4y and 5, 1, 3 is perpendicular to the plane 2 x y z 1.
(b) In what points does this line intersect the coordinate
planes? 20. L 1: x 2, 3 and parallel to the plane 12 32. The plane through the origin and the points 2, 16. (a) Find parametric equations for the line through 5, 1, 0 that 17. Find a vector equation for the line segment from 2, 5 and parallel to the 1, 6, 0 31. The plane through the points 0, 1, 1 , 1, 0, 1 , and 1, 1, 0 the point 0, 2, 1 and is parallel to the line with parametric equations x 1 2 t, y 3 t, z 5 7t.
(b) Find the points in which the required line in part (a) intersects the coordinate planes. 1 7z 3x 15. (a) Find symmetric equations for the line that passes through 19. L 1: x 2 and is parallel to the plane 2 x 1 and 2, 5, 3 perpendicular to the
3, 2, 0 and 5, 1, 4 ? line through z y 30. The plane that contains the line x 14. Is the line through 4, 1, L 2: x 1 29. The plane through the point 4, ■ 13. Is the line through 19–22 3z y plane x 0 ■ to 5, 6, 2, 8, 10 and perpendicular to
4 3t 2 t, z t, y 28. The plane through the point z and x 1 27. The plane through the origin and parallel to the plane 1, 1 and parallel to the line 12. The line of intersection of the planes x 1, 1 and with normal vector k 26. The plane through the point j k 11. The line through 1, j 3 and with normal 2k 25. The plane through the point 1, 3 10. The line through 2, 1, 0 and perpendicular to both i and j 2, 1, 5 vector 6. The line through the origin and the point 1, 2, 3 ■ Find an equation of the plane.  ■ ■ ■ ■ ■ ■ and x 2y 3z 1. y z 0 5E13(pp 858867) 1/18/06 11:33 AM Page 867 ❙❙❙❙ S ECTION 13.5 EQUATIONS OF LINES AND PLANES 45–50  Determine whether the...
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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 at Austin.
 Fall '09
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