Which of the following planes intersects the planes $x-y+2z =3$ and $4x+3y-z=1$ along the same line?

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Which of the following planes intersects the planes $x-y+2z =3$ and $4x+3y-z=1$ along the same line?



$a)space 11x+10y-5z=0$



$b)space 7x+7y-4z=0$



$c)space 5x+2y+z=2$




vectors




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  • 1




    Row reduction of an appropriate matrix is not a magical cure-all for every linear algebra problem, but this problem is yet another of the many examples where it works wonders. See if you can figure out how and why.
    – JMoravitz
    Jul 27 at 4:13











  • Just find the line of intersection with both these planes for all parts and see which gives the same equation of the line.
    – Devendra Singh Rana
    Jul 27 at 4:31














up vote
0
down vote

favorite












Which of the following planes intersects the planes $x-y+2z =3$ and $4x+3y-z=1$ along the same line?



$a)space 11x+10y-5z=0$



$b)space 7x+7y-4z=0$



$c)space 5x+2y+z=2$




vectors




share|cite|improve this question

















  • 1




    Row reduction of an appropriate matrix is not a magical cure-all for every linear algebra problem, but this problem is yet another of the many examples where it works wonders. See if you can figure out how and why.
    – JMoravitz
    Jul 27 at 4:13











  • Just find the line of intersection with both these planes for all parts and see which gives the same equation of the line.
    – Devendra Singh Rana
    Jul 27 at 4:31












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Which of the following planes intersects the planes $x-y+2z =3$ and $4x+3y-z=1$ along the same line?



$a)space 11x+10y-5z=0$



$b)space 7x+7y-4z=0$



$c)space 5x+2y+z=2$




vectors




share|cite|improve this question













Which of the following planes intersects the planes $x-y+2z =3$ and $4x+3y-z=1$ along the same line?



$a)space 11x+10y-5z=0$



$b)space 7x+7y-4z=0$



$c)space 5x+2y+z=2$





vectors





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 27 at 4:57









高田航

1,116318




1,116318









asked Jul 27 at 4:03









Seylin

445




445







  • 1




    Row reduction of an appropriate matrix is not a magical cure-all for every linear algebra problem, but this problem is yet another of the many examples where it works wonders. See if you can figure out how and why.
    – JMoravitz
    Jul 27 at 4:13











  • Just find the line of intersection with both these planes for all parts and see which gives the same equation of the line.
    – Devendra Singh Rana
    Jul 27 at 4:31












  • 1




    Row reduction of an appropriate matrix is not a magical cure-all for every linear algebra problem, but this problem is yet another of the many examples where it works wonders. See if you can figure out how and why.
    – JMoravitz
    Jul 27 at 4:13











  • Just find the line of intersection with both these planes for all parts and see which gives the same equation of the line.
    – Devendra Singh Rana
    Jul 27 at 4:31







1




1




Row reduction of an appropriate matrix is not a magical cure-all for every linear algebra problem, but this problem is yet another of the many examples where it works wonders. See if you can figure out how and why.
– JMoravitz
Jul 27 at 4:13





Row reduction of an appropriate matrix is not a magical cure-all for every linear algebra problem, but this problem is yet another of the many examples where it works wonders. See if you can figure out how and why.
– JMoravitz
Jul 27 at 4:13













Just find the line of intersection with both these planes for all parts and see which gives the same equation of the line.
– Devendra Singh Rana
Jul 27 at 4:31




Just find the line of intersection with both these planes for all parts and see which gives the same equation of the line.
– Devendra Singh Rana
Jul 27 at 4:31










1 Answer
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We have $x=3+y-2z$ putting this in the second equation we get $$4(3+y-2z)+3y-z=1 \ 7y-9z=-11$$



Take $z=t$ and we get equation of line as $$(frac-5t+107,frac9t-117, t)$$



$$11timesfrac-5t+107+10timesfrac9t-117- 5t=frac-55t+110+90t-110-35t
7=0$$
Hence it is the first option






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    We have $x=3+y-2z$ putting this in the second equation we get $$4(3+y-2z)+3y-z=1 \ 7y-9z=-11$$



    Take $z=t$ and we get equation of line as $$(frac-5t+107,frac9t-117, t)$$



    $$11timesfrac-5t+107+10timesfrac9t-117- 5t=frac-55t+110+90t-110-35t
    7=0$$
    Hence it is the first option






    share|cite|improve this answer

























      up vote
      1
      down vote













      We have $x=3+y-2z$ putting this in the second equation we get $$4(3+y-2z)+3y-z=1 \ 7y-9z=-11$$



      Take $z=t$ and we get equation of line as $$(frac-5t+107,frac9t-117, t)$$



      $$11timesfrac-5t+107+10timesfrac9t-117- 5t=frac-55t+110+90t-110-35t
      7=0$$
      Hence it is the first option






      share|cite|improve this answer























        up vote
        1
        down vote










        up vote
        1
        down vote









        We have $x=3+y-2z$ putting this in the second equation we get $$4(3+y-2z)+3y-z=1 \ 7y-9z=-11$$



        Take $z=t$ and we get equation of line as $$(frac-5t+107,frac9t-117, t)$$



        $$11timesfrac-5t+107+10timesfrac9t-117- 5t=frac-55t+110+90t-110-35t
        7=0$$
        Hence it is the first option






        share|cite|improve this answer













        We have $x=3+y-2z$ putting this in the second equation we get $$4(3+y-2z)+3y-z=1 \ 7y-9z=-11$$



        Take $z=t$ and we get equation of line as $$(frac-5t+107,frac9t-117, t)$$



        $$11timesfrac-5t+107+10timesfrac9t-117- 5t=frac-55t+110+90t-110-35t
        7=0$$
        Hence it is the first option







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Jul 27 at 5:53









        Piyush Divyanakar

        3,258122




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