How do I find a tangent plane without a specified point?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite
2












I was having a problem finding the points on $z=3x^2 - 4y^2$ where vector $n=<3,2,2>$ is normal to the tangent plane.



How do we calculate the tangent plane equation without a specific point to calculate it at?



I also had an idea to take the cross product of $2$ vectors in the plane and somehow compare it to the $n$ vector but I don't know exactly how to do this. Thank you for any help!






multivariable-calculus vectors orthonormal tangent-spaces







share|cite|improve this question























  • Set $x=0$ and $y=0$ in the eqution anc compute $z$. This is a point.
    – Mauro ALLEGRANZA
    2 hours ago











  • I don't think that is exactly what the OP is asking!
    – user247327
    1 hour ago














up vote
2
down vote

favorite
2












I was having a problem finding the points on $z=3x^2 - 4y^2$ where vector $n=<3,2,2>$ is normal to the tangent plane.



How do we calculate the tangent plane equation without a specific point to calculate it at?



I also had an idea to take the cross product of $2$ vectors in the plane and somehow compare it to the $n$ vector but I don't know exactly how to do this. Thank you for any help!






multivariable-calculus vectors orthonormal tangent-spaces







share|cite|improve this question























  • Set $x=0$ and $y=0$ in the eqution anc compute $z$. This is a point.
    – Mauro ALLEGRANZA
    2 hours ago











  • I don't think that is exactly what the OP is asking!
    – user247327
    1 hour ago












up vote
2
down vote

favorite
2









up vote
2
down vote

favorite
2






2





I was having a problem finding the points on $z=3x^2 - 4y^2$ where vector $n=<3,2,2>$ is normal to the tangent plane.



How do we calculate the tangent plane equation without a specific point to calculate it at?



I also had an idea to take the cross product of $2$ vectors in the plane and somehow compare it to the $n$ vector but I don't know exactly how to do this. Thank you for any help!






multivariable-calculus vectors orthonormal tangent-spaces







share|cite|improve this question















I was having a problem finding the points on $z=3x^2 - 4y^2$ where vector $n=<3,2,2>$ is normal to the tangent plane.



How do we calculate the tangent plane equation without a specific point to calculate it at?



I also had an idea to take the cross product of $2$ vectors in the plane and somehow compare it to the $n$ vector but I don't know exactly how to do this. Thank you for any help!






multivariable-calculus vectors orthonormal tangent-spaces




multivariable-calculus vectors orthonormal tangent-spaces






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 1 hour ago









hamza boulahia

881317




881317










asked 2 hours ago









sjfklsdafjks

1132




1132











  • Set $x=0$ and $y=0$ in the eqution anc compute $z$. This is a point.
    – Mauro ALLEGRANZA
    2 hours ago











  • I don't think that is exactly what the OP is asking!
    – user247327
    1 hour ago
















  • Set $x=0$ and $y=0$ in the eqution anc compute $z$. This is a point.
    – Mauro ALLEGRANZA
    2 hours ago











  • I don't think that is exactly what the OP is asking!
    – user247327
    1 hour ago















Set $x=0$ and $y=0$ in the eqution anc compute $z$. This is a point.
– Mauro ALLEGRANZA
2 hours ago





Set $x=0$ and $y=0$ in the eqution anc compute $z$. This is a point.
– Mauro ALLEGRANZA
2 hours ago













I don't think that is exactly what the OP is asking!
– user247327
1 hour ago




I don't think that is exactly what the OP is asking!
– user247327
1 hour ago










3 Answers
3






active

oldest

votes

















up vote
3
down vote



accepted










Let $f(x,y,z)=3x^2-4y^2-z$. Then your surface is $bigl(x,y,z)inmathbbR^3,$. You are after the points $(x,y,z)$ in that surface such that $nabla f(x,y,z)$ is a multiple of $(3,2,2)$. So, solve the system$$left{beginarrayl6x=3lambda\-8y=2lambda\-1=2lambda\3x^2-4y^2-z=0.endarrayright.$$






share|cite|improve this answer




















  • Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
    – sjfklsdafjks
    1 hour ago










  • I'm glad I could help.
    – José Carlos Santos
    1 hour ago

















up vote
3
down vote













Let $ f(x,y,z)=3x^2 - 4y^2 - z$ then the normal vector at $p_0(x_0,y_0,z_0)$ is
$$nabla f(p)=(f_x,f_y,f_z)_p$$
or
$$nabla f(p)=(6x_0,-8y_0,-1)$$
then
$$dfracnabla f(p)=dfracvecnvecn$$






share|cite|improve this answer




















  • Be aware that the signs of the vectors could differ!
    – weee
    1 hour ago










  • yes, equality with a $pm$.
    – Nosrati
    1 hour ago










  • And then how can we calculate the tangent plane?
    – manooooh
    1 hour ago










  • $p_0=(-frac14,-frac18,frac18)$.
    – Nosrati
    1 hour ago

















up vote
0
down vote













The problem does not ask you to find a tangent plane! It asks you to find points where the normal vector is parallel to <3, 2, 2>. The normal vector at any point of f(x,y,z)= constant is $nabla f$. Here $f(x, y, z)= 3x^2- 4y^2- z= 0$. Find $nabla f$ and set it equal to <3k, 2k, 2k> for some k.






share|cite|improve this answer




















    Your Answer





    StackExchange.ifUsing("editor", function ()
    return StackExchange.using("mathjaxEditing", function ()
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    );
    );
    , "mathjax-editing");

    StackExchange.ready(function()
    var channelOptions =
    tags: "".split(" "),
    id: "69"
    ;
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function()
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled)
    StackExchange.using("snippets", function()
    createEditor();
    );

    else
    createEditor();

    );

    function createEditor()
    StackExchange.prepareEditor(
    heartbeatType: 'answer',
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader:
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    ,
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    );



    );













     

    draft saved


    draft discarded


















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2988636%2fhow-do-i-find-a-tangent-plane-without-a-specified-point%23new-answer', 'question_page');

    );

    Post as a guest

















    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    3
    down vote



    accepted










    Let $f(x,y,z)=3x^2-4y^2-z$. Then your surface is $bigl(x,y,z)inmathbbR^3,$. You are after the points $(x,y,z)$ in that surface such that $nabla f(x,y,z)$ is a multiple of $(3,2,2)$. So, solve the system$$left{beginarrayl6x=3lambda\-8y=2lambda\-1=2lambda\3x^2-4y^2-z=0.endarrayright.$$






    share|cite|improve this answer




















    • Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
      – sjfklsdafjks
      1 hour ago










    • I'm glad I could help.
      – José Carlos Santos
      1 hour ago














    up vote
    3
    down vote



    accepted










    Let $f(x,y,z)=3x^2-4y^2-z$. Then your surface is $bigl(x,y,z)inmathbbR^3,$. You are after the points $(x,y,z)$ in that surface such that $nabla f(x,y,z)$ is a multiple of $(3,2,2)$. So, solve the system$$left{beginarrayl6x=3lambda\-8y=2lambda\-1=2lambda\3x^2-4y^2-z=0.endarrayright.$$






    share|cite|improve this answer




















    • Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
      – sjfklsdafjks
      1 hour ago










    • I'm glad I could help.
      – José Carlos Santos
      1 hour ago












    up vote
    3
    down vote



    accepted







    up vote
    3
    down vote



    accepted






    Let $f(x,y,z)=3x^2-4y^2-z$. Then your surface is $bigl(x,y,z)inmathbbR^3,$. You are after the points $(x,y,z)$ in that surface such that $nabla f(x,y,z)$ is a multiple of $(3,2,2)$. So, solve the system$$left{beginarrayl6x=3lambda\-8y=2lambda\-1=2lambda\3x^2-4y^2-z=0.endarrayright.$$






    share|cite|improve this answer












    Let $f(x,y,z)=3x^2-4y^2-z$. Then your surface is $bigl(x,y,z)inmathbbR^3,$. You are after the points $(x,y,z)$ in that surface such that $nabla f(x,y,z)$ is a multiple of $(3,2,2)$. So, solve the system$$left{beginarrayl6x=3lambda\-8y=2lambda\-1=2lambda\3x^2-4y^2-z=0.endarrayright.$$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 1 hour ago









    José Carlos Santos

    136k17109198




    136k17109198











    • Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
      – sjfklsdafjks
      1 hour ago










    • I'm glad I could help.
      – José Carlos Santos
      1 hour ago
















    • Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
      – sjfklsdafjks
      1 hour ago










    • I'm glad I could help.
      – José Carlos Santos
      1 hour ago















    Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
    – sjfklsdafjks
    1 hour ago




    Just wanted to clarify for others that I used the bottom-most equation after getting x and y from the top 2 equations and lambda from the third one. Thank you for the answer!!
    – sjfklsdafjks
    1 hour ago












    I'm glad I could help.
    – José Carlos Santos
    1 hour ago




    I'm glad I could help.
    – José Carlos Santos
    1 hour ago










    up vote
    3
    down vote













    Let $ f(x,y,z)=3x^2 - 4y^2 - z$ then the normal vector at $p_0(x_0,y_0,z_0)$ is
    $$nabla f(p)=(f_x,f_y,f_z)_p$$
    or
    $$nabla f(p)=(6x_0,-8y_0,-1)$$
    then
    $$dfracnabla f(p)=dfracvecnvecn$$






    share|cite|improve this answer




















    • Be aware that the signs of the vectors could differ!
      – weee
      1 hour ago










    • yes, equality with a $pm$.
      – Nosrati
      1 hour ago










    • And then how can we calculate the tangent plane?
      – manooooh
      1 hour ago










    • $p_0=(-frac14,-frac18,frac18)$.
      – Nosrati
      1 hour ago














    up vote
    3
    down vote













    Let $ f(x,y,z)=3x^2 - 4y^2 - z$ then the normal vector at $p_0(x_0,y_0,z_0)$ is
    $$nabla f(p)=(f_x,f_y,f_z)_p$$
    or
    $$nabla f(p)=(6x_0,-8y_0,-1)$$
    then
    $$dfracnabla f(p)=dfracvecnvecn$$






    share|cite|improve this answer




















    • Be aware that the signs of the vectors could differ!
      – weee
      1 hour ago










    • yes, equality with a $pm$.
      – Nosrati
      1 hour ago










    • And then how can we calculate the tangent plane?
      – manooooh
      1 hour ago










    • $p_0=(-frac14,-frac18,frac18)$.
      – Nosrati
      1 hour ago












    up vote
    3
    down vote










    up vote
    3
    down vote









    Let $ f(x,y,z)=3x^2 - 4y^2 - z$ then the normal vector at $p_0(x_0,y_0,z_0)$ is
    $$nabla f(p)=(f_x,f_y,f_z)_p$$
    or
    $$nabla f(p)=(6x_0,-8y_0,-1)$$
    then
    $$dfracnabla f(p)=dfracvecnvecn$$






    share|cite|improve this answer












    Let $ f(x,y,z)=3x^2 - 4y^2 - z$ then the normal vector at $p_0(x_0,y_0,z_0)$ is
    $$nabla f(p)=(f_x,f_y,f_z)_p$$
    or
    $$nabla f(p)=(6x_0,-8y_0,-1)$$
    then
    $$dfracnabla f(p)=dfracvecnvecn$$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 1 hour ago









    Nosrati

    25.1k62052




    25.1k62052











    • Be aware that the signs of the vectors could differ!
      – weee
      1 hour ago










    • yes, equality with a $pm$.
      – Nosrati
      1 hour ago










    • And then how can we calculate the tangent plane?
      – manooooh
      1 hour ago










    • $p_0=(-frac14,-frac18,frac18)$.
      – Nosrati
      1 hour ago
















    • Be aware that the signs of the vectors could differ!
      – weee
      1 hour ago










    • yes, equality with a $pm$.
      – Nosrati
      1 hour ago










    • And then how can we calculate the tangent plane?
      – manooooh
      1 hour ago










    • $p_0=(-frac14,-frac18,frac18)$.
      – Nosrati
      1 hour ago















    Be aware that the signs of the vectors could differ!
    – weee
    1 hour ago




    Be aware that the signs of the vectors could differ!
    – weee
    1 hour ago












    yes, equality with a $pm$.
    – Nosrati
    1 hour ago




    yes, equality with a $pm$.
    – Nosrati
    1 hour ago












    And then how can we calculate the tangent plane?
    – manooooh
    1 hour ago




    And then how can we calculate the tangent plane?
    – manooooh
    1 hour ago












    $p_0=(-frac14,-frac18,frac18)$.
    – Nosrati
    1 hour ago




    $p_0=(-frac14,-frac18,frac18)$.
    – Nosrati
    1 hour ago










    up vote
    0
    down vote













    The problem does not ask you to find a tangent plane! It asks you to find points where the normal vector is parallel to <3, 2, 2>. The normal vector at any point of f(x,y,z)= constant is $nabla f$. Here $f(x, y, z)= 3x^2- 4y^2- z= 0$. Find $nabla f$ and set it equal to <3k, 2k, 2k> for some k.






    share|cite|improve this answer
























      up vote
      0
      down vote













      The problem does not ask you to find a tangent plane! It asks you to find points where the normal vector is parallel to <3, 2, 2>. The normal vector at any point of f(x,y,z)= constant is $nabla f$. Here $f(x, y, z)= 3x^2- 4y^2- z= 0$. Find $nabla f$ and set it equal to <3k, 2k, 2k> for some k.






      share|cite|improve this answer






















        up vote
        0
        down vote










        up vote
        0
        down vote









        The problem does not ask you to find a tangent plane! It asks you to find points where the normal vector is parallel to <3, 2, 2>. The normal vector at any point of f(x,y,z)= constant is $nabla f$. Here $f(x, y, z)= 3x^2- 4y^2- z= 0$. Find $nabla f$ and set it equal to <3k, 2k, 2k> for some k.






        share|cite|improve this answer












        The problem does not ask you to find a tangent plane! It asks you to find points where the normal vector is parallel to <3, 2, 2>. The normal vector at any point of f(x,y,z)= constant is $nabla f$. Here $f(x, y, z)= 3x^2- 4y^2- z= 0$. Find $nabla f$ and set it equal to <3k, 2k, 2k> for some k.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 1 hour ago









        user247327

        10.2k1515




        10.2k1515



























             

            draft saved


            draft discarded















































             


            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2988636%2fhow-do-i-find-a-tangent-plane-without-a-specified-point%23new-answer', 'question_page');

            );

            Post as a guest
































































            Comments

            Post a Comment

            Popular posts from this blog

            What does second last employer means? [closed]

            Image
            Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote -3 down vote favorite Say, for example I have worked in the following companies, Company A => 2010 - 2011 Company B => 2011 - 2012 Company C => 2012 - Till Date Company D => Have offer Now assume Company D is asking to submit documents from my second last employer. So from the list of companies given, which company would be qualified as second last employer? software-industry employer share | improve this question asked Aug 10 '14 at 5:16 Rajaprabhu Aravindasamy 559 1 6 13 closed as off-topic by Jim G., jmort253 ♦ Aug 11 '14 at 1:58 This question appears to be off-topic. The users who voted to close gave this specific reason: "Questions seeking advice on company-specific regulations, agreements, or policies should be directed to your manager or HR department. Questions that address...
            Read more

            Installing NextGIS Connect into QGIS 3?

            Image
            Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 1 down vote favorite Just acquired free version of NEXTGIS and trying to install the plugin for QGIS. It tells me it was not designed for version 3 of QGIS. How do I set up the QGIS-NEXTGIS interface then? qgis qgis-plugins nextgis share | improve this question edited 3 hours ago PolyGeo ♦ 51.9k 17 77 233 asked 4 hours ago IanGS 16 4 New contributor IanGS is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. add a comment  |  up vote 1 down vote favorite Just acquired free version of NEXTGIS and trying to install the plugin for QGIS. It tells me it was not designed for version 3 of QGIS. How do I set up the QGIS-NEXTGIS interface then? qgis qgis-plugin...
            Read more

            One-line joke

            A one-liner is a joke that is delivered in a single line. A good one-liner is said to be pithy - concise and meaningful. [1] Comedians and actors use this comedic method as part of their act, e.g. Jimmy Carr, Tommy Cooper, Rodney Dangerfield, Norm Macdonald, Ken Dodd, Stewart Francis, Zach Galifianakis, Mitch Hedberg, Anthony Jeselnik, Milton Jones, Shappi Khorsandi, Jay London, Mark Linn-Baker, Demetri Martin, Groucho Marx, Dan Mintz, Emo Philips, Tim Vine, Steven Wright and Henny Youngman and Arnold Schwarzenegger. [ citation needed ] Many fictional characters are also known to deliver one-liners, including James Bond, who usually includes pithy and laconic quips after disposing of a villain. [ citation needed ] Examples "A baby seal walks into a club." "A dyslexic man walks into a bra." (Anonymous) "There are three types of people, those who can count and those who can't." "Venison's dear, isn't it?" (Jimmy Carr) "An escala...
            Read more