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19-22 Determine whether the lines L₁ and L₂ are parallel, skew, or intersecting. If they intersect, find the point of intersection. 19. L₁: x= 3 + 2t, y = 4-t, z = 1 + 3t L₂: x = 1 + 4s, y = 3 - 2s, z = 4 + 5s

19-22 Determine whether the lines L₁ and L₂ are parallel, skew, or intersecting. If they intersect, find the point of intersection. 19. L₁: x= 3 + 2t, y = 4-t, z = 1 + 3t L₂: x = 1 + 4s, y = 3 - 2s, z = 4 + 5s

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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Question

19

 

08 ne. line e the 17. Find a vector equation for the line segment from (6, -1,9) to (7, 6, 0). 18. Find parametric equations for the line segment from (-2, 18, 31) to (11, -4, 48). 19-22 Determine whether the lines L₁ and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection. 19. L₁: x = 3 + 2t, y = 4-t, z = 1 + 3t L₂: x= 1 + 4s, y = 3 - 2s, z = 4 + 5s mishale str. 28 20. L₁: x = 5 - 12t, y = 3 + 9t, z = 13tdcb L₂: x = 3 + 8s, y=-6s, z = 7+2s 1 21. L₁: x-²-2-2---3 2 L2: 22. L₁: L2: 1 x-3 1 X y + 4 y - 1 - 1 1 x - 2 2 3 adq z - 2 al-7 z - 2 3 y-3 -2 A Z 7 Veously +1-90011 23-40 Find an equation of the plane. 23. The plane through the origin and perpendicular to the vector (1, -2, 5) 24. The plane through the point (5, 3, 5) and with normal vector 2 i + j - k 25. The plane through the point (-1, 2, 3) and with normal vector i +4j + k 26. The plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y = 2-t, z = 3 + 4t 27. The plane through the point (1,-1,-1) and parallel to the plane 5x - y -z = 6
Transcribed Image Text:08 ne. line e the 17. Find a vector equation for the line segment from (6, -1,9) to (7, 6, 0). 18. Find parametric equations for the line segment from (-2, 18, 31) to (11, -4, 48). 19-22 Determine whether the lines L₁ and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection. 19. L₁: x = 3 + 2t, y = 4-t, z = 1 + 3t L₂: x= 1 + 4s, y = 3 - 2s, z = 4 + 5s mishale str. 28 20. L₁: x = 5 - 12t, y = 3 + 9t, z = 13tdcb L₂: x = 3 + 8s, y=-6s, z = 7+2s 1 21. L₁: x-²-2-2---3 2 L2: 22. L₁: L2: 1 x-3 1 X y + 4 y - 1 - 1 1 x - 2 2 3 adq z - 2 al-7 z - 2 3 y-3 -2 A Z 7 Veously +1-90011 23-40 Find an equation of the plane. 23. The plane through the origin and perpendicular to the vector (1, -2, 5) 24. The plane through the point (5, 3, 5) and with normal vector 2 i + j - k 25. The plane through the point (-1, 2, 3) and with normal vector i +4j + k 26. The plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y = 2-t, z = 3 + 4t 27. The plane through the point (1,-1,-1) and parallel to the plane 5x - y -z = 6
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