29. Prove that the following systems intersect at a point and then determine the solution: П₁: 2x + y + 6z - 7 = 0 π1: П2: 3x+4y+3z+8=0 П3 x 2y 4z - 9 = 0 (x = 1-2t 27. In 3-space, find the distance between the skew lines y=1+t and [x, y, z] = [4, 7, 1] + t [1, 4, 2]. z = 4t (x = 7-t 28. Determine the intersection point of the line y = 2+t and the plane π: x + 2y + 3z − 15 = 0 (z = 4 - 3t
29. Prove that the following systems intersect at a point and then determine the solution: П₁: 2x + y + 6z - 7 = 0 π1: П2: 3x+4y+3z+8=0 П3 x 2y 4z - 9 = 0 (x = 1-2t 27. In 3-space, find the distance between the skew lines y=1+t and [x, y, z] = [4, 7, 1] + t [1, 4, 2]. z = 4t (x = 7-t 28. Determine the intersection point of the line y = 2+t and the plane π: x + 2y + 3z − 15 = 0 (z = 4 - 3t
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 35E
Question
![29. Prove that the following systems intersect at a point and then determine the solution:
П₁: 2x + y + 6z - 7 = 0
π1:
П2: 3x+4y+3z+8=0
П3 x 2y 4z - 9 = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2F04f48464-ff71-48a0-a753-712c6f480d54%2Fbjky7s_processed.png&w=3840&q=75)
Transcribed Image Text:29. Prove that the following systems intersect at a point and then determine the solution:
П₁: 2x + y + 6z - 7 = 0
π1:
П2: 3x+4y+3z+8=0
П3 x 2y 4z - 9 = 0
![(x = 1-2t
27. In 3-space, find the distance between the skew lines y=1+t and [x, y, z] = [4, 7, 1] + t [1, 4, 2].
z = 4t
(x = 7-t
28. Determine the intersection point of the line y = 2+t and the plane π: x + 2y + 3z − 15 = 0
(z = 4 - 3t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2F04f48464-ff71-48a0-a753-712c6f480d54%2F9zjvfr_processed.png&w=3840&q=75)
Transcribed Image Text:(x = 1-2t
27. In 3-space, find the distance between the skew lines y=1+t and [x, y, z] = [4, 7, 1] + t [1, 4, 2].
z = 4t
(x = 7-t
28. Determine the intersection point of the line y = 2+t and the plane π: x + 2y + 3z − 15 = 0
(z = 4 - 3t
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