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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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TRANSCRIBE THE FOLOWING TEXT IN DIGITAL FORMAT
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
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