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