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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
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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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
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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