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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    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






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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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      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






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      asked Apr 21 '16 at 11:58









      Ampatishan Arun

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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
          $$
          ell(t)=(0,1,-1)+t(1,-3,2)
          $$






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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
            $$
            ell(t)=(0,1,-1)+t(1,-3,2)
            $$






            share|cite|improve this answer
























              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
              $$
              ell(t)=(0,1,-1)+t(1,-3,2)
              $$






              share|cite|improve this answer






















                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
                $$
                ell(t)=(0,1,-1)+t(1,-3,2)
                $$






                share|cite|improve this answer












                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
                $$
                ell(t)=(0,1,-1)+t(1,-3,2)
                $$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Apr 21 '16 at 13:51









                boaz

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