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Re: Vectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124238] Re: Vectors
  • From: "Nasser M. Abbasi" <nma at 12000.org>
  • Date: Sat, 14 Jan 2012 17:06:57 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jercnt$1eb$1@smc.vnet.net>
  • Reply-to: nma at 12000.org

On 1/14/2012 2:01 AM, Harry Har wrote:
> Hi All,
>
> I'm a math senior high school teacher, and I wish to understand how
> using mathematica 7 to find "h" and the intersection point between the
> plane 6x-2y+z=11 which contains the line x-1 = (y+1)/2 = (z-3)/h. Also
> how to plot/show it visually in 3D graph.
>
> Many thank's.
>
> Harry.
>

I am not sure what the rule of "h" there. When you say find "h", find
it to meet which criteria?

But here is a quick Manipulate that you can use to change h, and see
if it makes any sense to you. I hope I understood correctly what
you are saying. (just make sure you do not use h=0, to avoid divide by
zero). I made the slider start from 0.01

I put a red ball at the interestion of the surface and the 3 lines. You
can use the mouse to rotate, and use CTRL key with the mouse to zoom in/out.

----------------------------------
Manipulate[
  Module[{surface, eq1, eq2, eq3, sol, p1, to, d = 5},
   surface = 6 x - 2 y + z == 11;
   eq1 = x - 1 == 0;
   pt1 = {x /. First@Solve[eq1, x], 0, 0};
   eq2 = (y + 1)/2 == 0;
   pt2 = {0, y /. First@Solve[eq2, y], 0};
   eq3 = (z - 3)/h == 0;
   pt3 = {0, 0, z /. First@Solve[eq3, z]};
   
   sol = First@Solve[{surface, eq1, eq2, eq3}, {x, y, z}];
   to = {x, y, z} /. sol;
   
   p1 = ContourPlot3D[Evaluate@eq1, {x, -d, d}, {y, -d, d}, {z, -d, d},
      ImageSize -> 400, SphericalRegion -> True,
     PreserveImageOptions -> True, PlotRange -> Automatic,
     AxesLabel -> {"x", "y", "z"}, BoxRatios -> {4, 5, 3},
     ImagePadding -> {{10, 10}, {10, 35}},
     PlotLabel -> Row[{"solution is ", sol}]];
   
   
   Show[p1,
    Graphics3D[{
      {Red, Sphere[to, 0.15]},
      {Blue, Thickness -> 0.02, Line[{pt1, to}]},
      {Blue, Thickness -> 0.02, Line[{pt2, to}]},
      {Blue, Thickness -> 0.02, Line[{pt3, to}]}
      }]
    ]
   ],
  
  {{h, 0.01, "h="}, 0.01, 10, 0.1, Appearance -> "Labeled"}
  ]
------------------------------------------------

--Nasser



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