[College - Calculus III] Vectors and Planes

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  • argo15
    FFR Veteran
    • May 2006
    • 1863
    #1

    [College - Calculus III] Vectors and Planes

    Gosh, it might be a brain fart but I can't figure out how to do this.

    Code:
    Find a vector equation and parametric equations in t for the line through the point and perpendicular to the given plane. (P0 corresponds to t = 0.)
P0 = (4, 0, 7)
x + 2y + z = 6
v = ?i + ?j + ?k
x = ?
y = ?
z = ?
    Answers or anything that might send me in the right direction would be awesome. =)
    Tags: None
    • JKPolk
      tool
      • Aug 2003
      • 3737
      #2
      Re: [College - Calculus III] Vectors and Planes

      Have you tried taking the derivative with respect to each of the values and plugging in the intial conditions?

        Comment

        • argo15
          FFR Veteran
          • May 2006
          • 1863
          #3
          Re: [College - Calculus III] Vectors and Planes

          I don't think that is what he is looking for since this assignment is in the chapter before derivatives of vectors. Dot products or cross products are probably involved.

            Comment

            • dooty_7
              FFR Player
              • Jun 2005
              • 462
              #4
              Re: [College - Calculus III] Vectors and Planes

              I haven't done this for a while, so I hope what I say is not complete gibberish lol

              For the equation of a plane, aren't the coefficients simply the normal (perpendicular) to the plane? If so then we have P0 = 4,0,7 and normal 1,2,2.

              Leading us to get the general equation r = (4,0,7) + t(1,2,2)
              so x = 4 + t
              y = 2t
              z = 7 + 2t

                Comment

                • foilman8805
                  smoke wheat hail satin
                  FFR Simfile Author
                  • Sep 2006
                  • 5704
                  #5
                  Re: [College - Calculus III] Vectors and Planes

                  Originally posted by dooty_7
                  I haven't done this for a while, so I hope what I say is not complete gibberish lol

                  For the equation of a plane, aren't the coefficients simply the normal (perpendicular) to the plane? If so then we have P0 = 4,0,7 and normal 1,2,2.

                  Leading us to get the general equation r = (4,0,7) + t(1,2,2)
                  so x = 4 + t
                  y = 2t
                  z = 7 + 2t
                  Normal for the given plane is 1, 2, 1. I know it's a mistake though. You didn't mean to do that on purpose.

                  As a result the parametrics change to:

                  x = 4 + t
                  y = 2t
                  z = 7 + t

                  So, v is going to then be a substitution of the parametrics back into i, j, k form? I don't remember either lol...

                  EDIT: Yeah, I think v = (4 + t)i + (2t)j + (7 + t)k
                  Last edited by foilman8805; 09-29-2009, 01:10 PM.

                    Comment

                    • argo15
                      FFR Veteran
                      • May 2006
                      • 1863
                      #6
                      Re: [College - Calculus III] Vectors and Planes

                      Yeah, your right thank you =).

                      Answer was v= (4+t)i + (2t)j + (7+t)k

                      If I have any more issues I'll edit it in here. (math can be a bitch sometimes)

                        Comment

                        • foilman8805
                          smoke wheat hail satin
                          FFR Simfile Author
                          • Sep 2006
                          • 5704
                          #7
                          Re: [College - Calculus III] Vectors and Planes

                          If you have more issues, bump the thread, otherwise we probably won't come back to look for it.

                            Comment

                            • dooty_7
                              FFR Player
                              • Jun 2005
                              • 462
                              #8
                              Re: [College - Calculus III] Vectors and Planes

                              lol brain fart on my part haha :P

                                Comment

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