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Student[LinearAlgebra]

 PlanePlot
 plot a plane and associated vectors

 Calling Sequence PlanePlot(P1, pt, opts) PlanePlot(P2, vars, opts)

Parameters

 P1 - Vector, set or list of Vectors, or Vector-valued function; specify the plane pt - (optional) Vector; point on the plane P2 - equation or algebraic expression; equation of the plane vars - list; names of the variables opts - plotting options or equation(s) of the form option=value where option is one of showbasis, basisoptions, shownearestpoint, nearestpointoptions, shownormal, normaloptions, showplane, planeoptions, showpoint, pointoptions, or Student[plot options]; specify options for the plot

Description

 • The PlanePlot(P1) command plots the plane defined by P1, together with a normal Vector to the plane.  The plane can be specified in one of three ways:
 * A 3-D Vector:  P1 is the normal to the plane.
 * A set or list of 3-D Vectors: P1 represents a basis for the plane. The set or list of Vectors must define a 2-D subspace of 3-D space.
 * A Vector-valued procedure: P1 must be a procedure that takes two numeric arguments and returns a 3-D Vector.  It is evaluated at the arguments $0,0$, $1,0$, and $0,1$ to obtain points that define the plane.
 • In each of the first two cases (where the plane is defined by either a normal Vector or a spanning set of Vectors), the optional argument pt, given as a 3-D Vector, can be used to specify a point on the plane.  If pt is not provided, the plane passes through the origin.
 • The PlanePlot(P2, vars) command plots the plane defined by P2, which must be an algebraic expression or algebraic equation that is linear in the 3 variables named in the vars parameter.  The vars parameter can be omitted if all 3 variables explicitly appear in P2; note that in this case the axis order is not determined.
 • The opts argument can contain any of the Student plot options or any of the following equations that set plot options.
 showbasis = true or false
 Specifies whether vectors which form a spanning set for the plane are plotted.  The vectors are drawn with their bases at the same point as the base of the normal vector. [Default: false unless the set-or-list-of-Vectors form of P1 is used]
 basisoptions = list
 Provides options (such as color, shape) used to plot the basis vectors for the plane.  Because the vectors are plotted using the plots[arrow] command, only corresponding options are allowed.
 shownearestpoint = true or false
 Specifies whether the vector from the origin to the point on the plane, which is nearest the origin, is plotted.  [Default: false]
 nearestpointoptions = list
 Provides options used to plot the nearest-point vector. Because the vector is plotted using the plots[arrow] command, only corresponding options are allowed.
 shownormal = true or false
 Specifies whether the normal vector to the plane is drawn.  If selected, this vector is drawn with its tail at the point described in the showpoint option, unless showpoint = false has been specified, in which case it is drawn with its base at the nearest point on the plane to the origin.  [Default: true]
 normaloptions = list
 Provides options used to plot the normal vector to the plane. Because the vector is plotted using the plots[arrow] command, only corresponding options are allowed.
 showplane = true or false
 Specifies whether to display the plane.  [Default: true]
 planeoptions = list
 Provides options (such as color, style, grid) used to plot the plane.  Any option valid for the plot3d command can be provided.
 showpoint = true or false
 Specifies whether the vector from the origin to the specified point on the plane is plotted.  If pt is provided, this point is the head of the vector.  If the procedure form of P1 is given, this point is the value of the procedure at $0,0$.  Otherwise, this point is the nearest point on the plane to the origin.  [Default:  true]
 pointoptions = list
 Provides options used to plot the vector from the origin to a distinguished point on the plane.  For information on how this point is determined, see the description for the showpoint option. Because the vector is plotted using the plots[arrow] command, only corresponding options are allowed.
 caption = anything
 A caption for the plot.
 The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > ${\mathrm{infolevel}}_{\mathrm{Student}[\mathrm{LinearAlgebra}]}≔1:$
 > $\mathrm{PlanePlot}\left(-3x+2y+z=-3,\left[x,y,z\right],\mathrm{normaloptions}=\left[\mathrm{shape}=\mathrm{harpoon}\right]\right)$
 normal vector: <-3., 2., 1.> equation of plane: -3.*x+2.*y+1.*z = -3. point on plane nearest origin: <.6429, -.4286, -.2143> basis vectors: <.5345, .8414, -.7929e-1>, <.2673, -.7929e-1, .9604>
 > $\mathrm{PlanePlot}\left(⟨1,2,3⟩,⟨1,-3,-1⟩,\mathrm{orientation}=\left[10,58\right],\mathrm{shownearestpoint},\mathrm{showbasis}\right)$
 normal vector: <1., 2., 3.> equation of plane: 1.*x+2.*y+3.*z = -8. point on plane nearest origin: <-.5714, -1.143, -1.714> basis vectors: <-1.773, 2.569, -1.122>, <-2.659, -1.122, 1.634>
 > $\mathrm{PlanePlot}\left(\left\{⟨1,3,5.⟩,⟨2,7,-1⟩\right\},⟨-3,2,-1⟩\right)$
 normal vector: <-5.171, 1.497, .1361> equation of plane: -5.171*x+1.497*y+.1361*z = 18.37 point on plane nearest origin: <-3.276, .9483, .8621e-1> basis vectors: <1., 3., 5.>, <2., 7., -1.>
 > $\mathrm{PlanePlot}\left(\left(s,t\right)→s⟨1,3,-5⟩+t⟨0.01,-0.02,0.01⟩+⟨13,2,1⟩,\mathrm{showbasis},\mathrm{shownearestpoint}\right)$
 normal vector: <6.372, 5.462, 4.551> equation of plane: 6.372*x+5.462*y+4.551*z = 98.31 point on plane nearest origin: <6.873, 5.891, 4.909> basis vectors: <5.385, -10.77, 5.385>, <2.230, 6.689, -11.15>

The command to create the plot from the Plotting Guide is

 > $\mathrm{PlanePlot}\left(⟨1,3,2⟩,\mathrm{showbasis}\right)$
 normal vector: <1., 3., 2.> equation of plane: 1.*x+3.*y+2.*z = 0. point on plane nearest origin: <0., 0., 0.> basis vectors: <-.8018, .4927, -.3382>, <-.5345, -.3382, .7745>