Equation of Plane in a unit cube given the normal and volume enclosed












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I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?



$ n_xx+n_yy+n_zz + d =0 $



How can I calculate the 'd' ?



enter image description here










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  • $begingroup$
    You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
    $endgroup$
    – John Wayland Bales
    Dec 7 '18 at 6:11










  • $begingroup$
    @JohnWaylandBales Thanks for this... Will check it out
    $endgroup$
    – Some_guy
    Dec 7 '18 at 6:17
















0












$begingroup$


I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?



$ n_xx+n_yy+n_zz + d =0 $



How can I calculate the 'd' ?



enter image description here










share|cite|improve this question









$endgroup$












  • $begingroup$
    You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
    $endgroup$
    – John Wayland Bales
    Dec 7 '18 at 6:11










  • $begingroup$
    @JohnWaylandBales Thanks for this... Will check it out
    $endgroup$
    – Some_guy
    Dec 7 '18 at 6:17














0












0








0





$begingroup$


I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?



$ n_xx+n_yy+n_zz + d =0 $



How can I calculate the 'd' ?



enter image description here










share|cite|improve this question









$endgroup$




I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?



$ n_xx+n_yy+n_zz + d =0 $



How can I calculate the 'd' ?



enter image description here







geometry






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 7 '18 at 5:19









Some_guySome_guy

213




213












  • $begingroup$
    You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
    $endgroup$
    – John Wayland Bales
    Dec 7 '18 at 6:11










  • $begingroup$
    @JohnWaylandBales Thanks for this... Will check it out
    $endgroup$
    – Some_guy
    Dec 7 '18 at 6:17


















  • $begingroup$
    You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
    $endgroup$
    – John Wayland Bales
    Dec 7 '18 at 6:11










  • $begingroup$
    @JohnWaylandBales Thanks for this... Will check it out
    $endgroup$
    – Some_guy
    Dec 7 '18 at 6:17
















$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11




$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11












$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17




$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17










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