1. Determin or false in R³. (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are paralle (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. (h) Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (1) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel.
1. Determin or false in R³. (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are paralle (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. (h) Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (1) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
1 pl
![12.5 EXERCISES
(a) Two lines parallel to a third line are parallel.
1. Determine whether each statement is true or false in R³.
(b) Two lines perpendicular to a third line are parallel.
Two planes parallel to a third plane are parallel.
(d) Two planes perpendicular to a third plane are parallel.
(e) Two lines parallel to a plane are parallel.
(f) Two lines perpendicular to a plane are parallel.
(g) Two planes parallel to a line are parallel.
(h) Two planes perpendicular to a line are parallel.
(i) Two planes either intersect or are parallel.
(j) Two lines either intersect or are parallel.
(k) A plane and a line either intersect or are parallel.
2-5 Find a vector equation and parametric equations for the line.
2. The line through the point (6, -5, 2) and parallel to the
vector (1, 3, -3)
3. The line through the point (2, 2.4, 3.5) and parallel to the
vector 3i+2j - k
4. The line through the point (0, 14, -10) and parallel to the line
x = -1 + 2t, y = 6 - 3t, z = 3 +9t
5. The line through the point (1, 0, 6) and perpendicular to the
plane x + 3y + z = 5
for the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad941f7b-34e1-41bc-b27d-c60dbcd610a1%2F2cc6bc2b-f8b3-4589-942a-46ae7d33ea3f%2Fr6z6tgd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12.5 EXERCISES
(a) Two lines parallel to a third line are parallel.
1. Determine whether each statement is true or false in R³.
(b) Two lines perpendicular to a third line are parallel.
Two planes parallel to a third plane are parallel.
(d) Two planes perpendicular to a third plane are parallel.
(e) Two lines parallel to a plane are parallel.
(f) Two lines perpendicular to a plane are parallel.
(g) Two planes parallel to a line are parallel.
(h) Two planes perpendicular to a line are parallel.
(i) Two planes either intersect or are parallel.
(j) Two lines either intersect or are parallel.
(k) A plane and a line either intersect or are parallel.
2-5 Find a vector equation and parametric equations for the line.
2. The line through the point (6, -5, 2) and parallel to the
vector (1, 3, -3)
3. The line through the point (2, 2.4, 3.5) and parallel to the
vector 3i+2j - k
4. The line through the point (0, 14, -10) and parallel to the line
x = -1 + 2t, y = 6 - 3t, z = 3 +9t
5. The line through the point (1, 0, 6) and perpendicular to the
plane x + 3y + z = 5
for the
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