Lines and Planes in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2KVEoJiM4NDc3O0YnLyUlc2l6ZUdRIzI0RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGQC1GIzYnLUkjbW5HRiQ2KFEiM0YnL0YzUSMyMEYnRjVGO0Y+RkFGMi9GOUY3RjsvRj9RJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9GP1Enbm9ybWFsRic=Equation of Plane Given Its Normal and One Point JSFH
<Text-field style="Heading 1" layout="Heading 1">Problem LP-6</Text-field>JSFH
Obtain an equation for the plane that passes through the point P: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, and has for its normal the vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2J1EiTkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUC1JI21uR0YkNiRRIjNGJ0Y+LUY7Ni1RIn5GJ0Y+RkBGQkZERkZGSEZKRkwvRk9RJjAuMGVtRicvRlJGZW4tRiw2J1EiaUYnRi9GMkY1RjgtRjs2LVEoJm1pbnVzO0YnRj5GQEZCRkRGRkZIRkpGTC9GT1EsMC4yMjIyMjIyZW1GJy9GUkZeby1GVDYkUSI1RidGPkZXLUYsNidRImpGJ0YvRjJGNUY4LUY7Ni1RIitGJ0Y+RkBGQkZERkZGSEZKRkxGXW9GX28tRlQ2JFEiMkYnRj5GVy1GLDYnUSJrRidGL0YyRjVGOEY+.
JSFH
<Text-field style="Heading 1" layout="Heading 1">Vector Solution</Text-field>Data for the problem:
JSFHObtain the equation of the plane:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Write 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Press the Enter key.Context Menu: Simplify\342\211\273Assuming RealLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Solution by Task Template</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Tools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualizations\342\211\273Plane Plot
Graph of a PlaneSpecify a plane in one of the following ways:EquationNormal vector and a pointTwo vectors in the plane (basis) and a pointObtain plot of plane andNormal vectorEquation of the planeTwo vectors in the planeThe point on the plane closest to the originThe number of digits in the returned data is controlled by the slider.Click the icon below to execute the PlanePlot command. Variables:
use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
module()
local temp1;
Do(temp1 = %MathContainer1);
if temp1=NULL then Do(%RadioButton0 = true);
Do(%RadioButton1 = false);
end if;
end module;
end use;
use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
module()
local temp1;
Do(temp1 = %MathContainer2);
if temp1=NULL then Do(%RadioButton0 = true);
Do(%RadioButton2 = false);
end if;
end module;
end use;
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 DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
module()
local temp1;
Do(temp1 = %MathContainer3);
if temp1=NULL then Do(%RadioButton0 = true);
Do(%RadioButton3 = false);
end if;
end module;
end use;
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYmLUYjNiYtRiw2Ji1GIzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRkMtRiM2JS1JI21uR0YkNiRRIjFGJy9GQlEnbm9ybWFsRicvRj9GPS9GQlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZMRkwvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnLUkjbW9HRiQ2LVEiLEYnRkwvJSZmZW5jZUdGQC8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0ZALyUqc3ltbWV0cmljR0ZALyUobGFyZ2VvcEdGQC8lLm1vdmFibGVsaW1pdHNHRkAvJSdhY2NlbnRHRkAvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYmLUYjNiQtRjU2JUY3LUYjNiUtRkk2JFEiMkYnRkxGTkZPRlFGTEZMRlRGV0ZMRkwvRlVRIltGJy9GWFEiXUYnRlotRiw2Ji1GIzYkLUY4NiVRIlBGJ0ZORk9GTEZMRlRGV0ZM
Digits = use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
Do(%Label0(caption) = %Slider0);
end use;
= use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
Do(%MathContainer0 = NULL);
Do(%MathContainer1 = NULL);
Do(%MathContainer2 = NULL);
Do(%MathContainer3 = NULL);
Do(%Slider0(value) = 4);
Do(%Label0(caption) = 4);
Do(%TextArea0 = NULL);
Do(%RadioButton0 = true);
Do(%RadioButton1(value) = false);
Do(%RadioButton2(value) = false);
Do(%RadioButton3(value) = false);
end use;
JSFH
infolevel[Student[LinearAlgebra]]:=1:
use DocumentTools,Student[LinearAlgebra] in
proc()
local temp1,VAR,p,P,N;
Do(%TextArea0 = NULL);
Do(temp1 = %MathContainer0);
if temp1=NULL then Do(%TextArea0 = "Provide 3 variables");return;
elif type([temp1],'list'('list'('name'))) then
\011if nops(indets(temp1))=3 then VAR:=temp1;
\011else Do(%TextArea0 = "Incorrect number of variables");return;
\011end if:
elif type([temp1],'list'('name')) then
\011if nops(indets([temp1]))=3 then VAR:=[temp1];
\011else Do(%TextArea0 = "Incorrect number of variables");return;
\011end if:
else Do(%TextArea0 = "Cannot fathom entry for variables");return;
end if:
if Do(%RadioButton1) then Do(P = %MathContainer1);
elif Do(%RadioButton2) then Do(P = %MathContainer2);
elif Do(%RadioButton3) then Do(P = %MathContainer3);
else Do(%TextArea0 = "Select one form of Plane");return;
end if;
Do(N = %Slider0);
SetDefault(infodigits=N):
if type([P],'list'(`=`)) or type([P],'list'(`+`)) then
plots[display](PlanePlot(P, VAR, axes = boxed, labels = VAR, showbasis, orientation = [-50, 65], title="",shownearestpoint, nearestpointoptions=[color=black]),axes=box,transparency=.6):
else plots[display](PlanePlot(P, axes = boxed, labels = VAR, showbasis, orientation = [-50, 65], planeoptions = [transparency = .8],title="",shownearestpoint, nearestpointoptions=[color=black]),axes=box):
end if;
end();
end use;
infolevel[Student[LinearAlgebra]]:=0:
Student[LinearAlgebra][SetDefault](infodigits=4):
JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=