\text{Zostrojte

\text{1. Kocku }ABCDEFGH:A(0,0,0);B(0,3,0)

\text{2. Stredy hrán hornej podstavy: }S_{EF},S_{FG},S_{GH},S_{EH}

\text{3. Stredy hrán }CG \text{ a } BC:\ S_{CG} ,\ S_{BC}

\text{4. Body P_{1/3}: (EHP_{1/3})=-2;  Q_{1/3}: (GCQ_{1/3})=-2

\text{ Určte vzájomnú polohu }

\overleftrightarrow{ CS_{FG}}\text{  a  }\overleftrightarrow{ P_{1/3}Q_{1/3}} \text{  ...}

\overleftrightarrow{ HS_{CG}}\text{  a  }\overleftrightarrow{ S_{EH}F} \text{    ...}

\overleftrightarrow{ S_{EH}D}\text{  a  }\overleftrightarrow{ EFS_{BC}} \text{    ...}

\overleftrightarrow{ S_{FG}B}\text{  a  }\overleftrightarrow{EFG} \text{   ...}

\overleftrightarrow{ BCH}\text{  a  }\overleftrightarrow{ S_{EH}S_{FG}D} \text{   ...}

\overleftrightarrow{ S_{GH}S_{EH}}\text{  a  }\overleftrightarrow{ECA} \text{    ...}

\text{Pomocou už vyznačených bodov zapíšte 3 rôzne roviny kolmé na }\overleftrightarrow{S_{BC}S_{CG}S_{EH}}

1. \; \overleftrightarrow{XXX}  \;\; \;\;   2. \; \overleftrightarrow{XXX}  \;\; \;\;  3. \; \overleftrightarrow{XXX} 

A = (0, 0, 0)
B = (3, 0, 0)
C = Point(Circle[B, Distance[A, B], Segment[A, B]])
a, D, E, F, G, H, stenaABCD, stenaADHE, stenaABFE, stenaBCGF, stenaCDHG, stenaEFGH, hranaAD, hranaAB, hranaBC, hranaCD, hranaAE, hranaDH, hranaEH, hranaEF, hranaBF, hranaFG, hranaCG, hranaGH = Cube(A, B, C)
S_{EF} = Midpoint(hranaEF)
S_{FG} = Midpoint(hranaFG)
S_{GH} = Midpoint(hranaGH)
S_{EH} = Midpoint(hranaEH)
S_{BC} = Midpoint(hranaBC)
S_{CG} = Midpoint(hranaCG)
P_{1/3}: (0, 2, 3)
Q_{1}: (0, 3, 1)
f = Line(Q_{1}, hranaCD)
Q_{1/3} = Intersect(f, hranaCG)