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Given Lines Line 21 3x + 11y188 = 0 Live 3 - 11x-3y +56=0 Line 1 - 3x + Hy + 15=0 3x -15 11 Live 3: ay line 2. 3x+lly +88 = 0 ny = -88-3x 11 dy.. dx Lines Lines are 11 B 11 -11x + 3y + 55-0 -y = -55+ 11x 3 ay ==111 slope of live 3 or m₂ = 1/ ; slope of line 1 or m₁ = 3 , slope of line 2 or m₂ = -3 31 parallel if slop of both lines are equal. between live sI and Live 2! m, & m₂: are perpendicular ext slope of both thes m₁ m₂ is m₁ 7m₂ and m₁m₂ # 1 following m, m₂.1 Hence, line I and live 2 are neither paralled or perpendicular. between Lue 2 and live 3: mg / m₂ 1 = M₂. m₂ 7-1 Hence non perpendicular line 1 mimg - 유 X Between Line & Live 2 and line 2 Hence, A Line I & line 3 are neither parallel are perpendicular to each other.

Given Lines Line 21 3x + 11y188 = 0 Live 3 - 11x-3y +56=0 Line 1 - 3x + Hy + 15=0 3x -15 11 Live 3: ay line 2. 3x+lly +88 = 0 ny = -88-3x 11 dy.. dx Lines Lines are 11 B 11 -11x + 3y + 55-0 -y = -55+ 11x 3 ay ==111 slope of live 3 or m₂ = 1/ ; slope of line 1 or m₁ = 3 , slope of line 2 or m₂ = -3 31 parallel if slop of both lines are equal. between live sI and Live 2! m, & m₂: are perpendicular ext slope of both thes m₁ m₂ is m₁ 7m₂ and m₁m₂ # 1 following m, m₂.1 Hence, line I and live 2 are neither paralled or perpendicular. between Lue 2 and live 3: mg / m₂ 1 = M₂. m₂ 7-1 Hence non perpendicular line 1 mimg - 유 X Between Line & Live 2 and line 2 Hence, A Line I & line 3 are neither parallel are perpendicular to each other.

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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Given lines Lune 1: Line 2 Line 3 : Line 1 : line 2: Line 8: "у -11x-3y 3x + 11 g + 88 = 0 3y+56=0 3 x. + Lines - 3x + 11y + 15 =0 3x -15 11 dy dx Lines - 11 x = dy dx y ³x+lly +88 = 0 ny = -88-3x пу /1 - зу dy = -=1/1/1 dx 115 = 0 are are - - y = -= 55+ 11x 3 3 11 = -3 +55=0 I slope of une 1 or m₁ = 3 1 slope of line 2 or M₂ = -3 }} I slope of line 3 between live 1 and Live 2! m, & m₂! or m₂ =-11 3 parallel if slope of both lines are equal. perpendicular if slope of both thes mi + m₂ is 2 m₁ m₂ and m₁m₂ # <1 following m, m₂ = 1 Hence, line I and live 2 are neether paralled or perpendicular Between Like 2 and live 3: mg 7 m₂ M2₂ m₂ -1 Live 2 and line 2 1 Hence non perpendicular. line 1 Between Line & A mi ma m₁ m3 = Hence, -)1. 3 Line I & line 3 11 are are neither parallel perpendicular to each other
Transcribed Image Text:Given lines Lune 1: Line 2 Line 3 : Line 1 : line 2: Line 8: "у -11x-3y 3x + 11 g + 88 = 0 3y+56=0 3 x. + Lines - 3x + 11y + 15 =0 3x -15 11 dy dx Lines - 11 x = dy dx y ³x+lly +88 = 0 ny = -88-3x пу /1 - зу dy = -=1/1/1 dx 115 = 0 are are - - y = -= 55+ 11x 3 3 11 = -3 +55=0 I slope of une 1 or m₁ = 3 1 slope of line 2 or M₂ = -3 }} I slope of line 3 between live 1 and Live 2! m, & m₂! or m₂ =-11 3 parallel if slope of both lines are equal. perpendicular if slope of both thes mi + m₂ is 2 m₁ m₂ and m₁m₂ # <1 following m, m₂ = 1 Hence, line I and live 2 are neether paralled or perpendicular Between Like 2 and live 3: mg 7 m₂ M2₂ m₂ -1 Live 2 and line 2 1 Hence non perpendicular. line 1 Between Line & A mi ma m₁ m3 = Hence, -)1. 3 Line I & line 3 11 are are neither parallel perpendicular to each other
Expert Solution
Step 1: Introduction of the given problem

Given lines

Line 1 colon space minus 3 x plus 11 y plus 15 equals 0

Line  2 colon space 3 x plus 11 y plus 88 equals 0

Line 3 colon space minus 11 x minus 3 y plus 55 equals 0

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