Find the equation of the line of intersection of two planes
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normally to find the intersecting line 3 planes will be provided but here only 2 planes are given, though i have to find 3 variables. please some one help me to find the equation of line of intersection
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asked Apr 21 '16 at 11:58
Ampatishan Arun
234
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up vote
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down vote
favorite
enter image description here
normally to find the intersecting line 3 planes will be provided but here only 2 planes are given, though i have to find 3 variables. please some one help me to find the equation of line of intersection
vectors
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
enter image description here
normally to find the intersecting line 3 planes will be provided but here only 2 planes are given, though i have to find 3 variables. please some one help me to find the equation of line of intersection
vectors
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
enter image description here
normally to find the intersecting line 3 planes will be provided but here only 2 planes are given, though i have to find 3 variables. please some one help me to find the equation of line of intersection
vectors
vectors
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
asked Apr 21 '16 at 11:58
Ampatishan Arun
234
234
add a comment |Â
add a comment |Â
1 Answer
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Writhing down the solutions of the system of equations of the two planes gives you directly their intersection line. e.g. if the planes are $x+y+z=0$ and $x-y-2z=1$, then from the first equation $z=-x-y$. Plug it in the second equation gives $x-y-2(-x-y)=1$, that is $3x+y=1$. Hence the solutions set is
$$
ell=(t,1-3t,2t-1):tin R=(0,1,-1)+t(1,-3,2):tin R
$$
so the parametric equation of the line is
$$
ell(t)=(0,1,-1)+t(1,-3,2)
$$
answered Apr 21 '16 at 13:51
boaz
2,293614
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Writhing down the solutions of the system of equations of the two planes gives you directly their intersection line. e.g. if the planes are $x+y+z=0$ and $x-y-2z=1$, then from the first equation $z=-x-y$. Plug it in the second equation gives $x-y-2(-x-y)=1$, that is $3x+y=1$. Hence the solutions set is
$$
ell=(t,1-3t,2t-1):tin R=(0,1,-1)+t(1,-3,2):tin R
$$
so the parametric equation of the line is
$$
ell(t)=(0,1,-1)+t(1,-3,2)
$$
answered Apr 21 '16 at 13:51
boaz
2,293614
add a comment |Â
up vote
0
down vote
Writhing down the solutions of the system of equations of the two planes gives you directly their intersection line. e.g. if the planes are $x+y+z=0$ and $x-y-2z=1$, then from the first equation $z=-x-y$. Plug it in the second equation gives $x-y-2(-x-y)=1$, that is $3x+y=1$. Hence the solutions set is
$$
ell=(t,1-3t,2t-1):tin R=(0,1,-1)+t(1,-3,2):tin R
$$
so the parametric equation of the line is
$$
ell(t)=(0,1,-1)+t(1,-3,2)
$$
answered Apr 21 '16 at 13:51
boaz
2,293614
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Writhing down the solutions of the system of equations of the two planes gives you directly their intersection line. e.g. if the planes are $x+y+z=0$ and $x-y-2z=1$, then from the first equation $z=-x-y$. Plug it in the second equation gives $x-y-2(-x-y)=1$, that is $3x+y=1$. Hence the solutions set is
$$
ell=(t,1-3t,2t-1):tin R=(0,1,-1)+t(1,-3,2):tin R
$$
so the parametric equation of the line is
$$
ell(t)=(0,1,-1)+t(1,-3,2)
$$
answered Apr 21 '16 at 13:51
boaz
2,293614
Writhing down the solutions of the system of equations of the two planes gives you directly their intersection line. e.g. if the planes are $x+y+z=0$ and $x-y-2z=1$, then from the first equation $z=-x-y$. Plug it in the second equation gives $x-y-2(-x-y)=1$, that is $3x+y=1$. Hence the solutions set is
$$
ell=(t,1-3t,2t-1):tin R=(0,1,-1)+t(1,-3,2):tin R
$$
so the parametric equation of the line is
$$
ell(t)=(0,1,-1)+t(1,-3,2)
$$
answered Apr 21 '16 at 13:51
boaz
2,293614
answered Apr 21 '16 at 13:51
boaz
2,293614
answered Apr 21 '16 at 13:51
boaz
2,293614
answered Apr 21 '16 at 13:51
boaz
2,293614
2,293614
add a comment |Â
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