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20 hodin výuky
1. Analytická geometrie lineárních útvarů (5 hodin)
2 hodiny
řekli jsme si, jak zapsat bod, jak ze dvou bodů zapsat vektor, jak pomocí vektoru a bodu zapsat rovnici přímky (směrový vektor-parametrické rovnice; normálový vektor-obecná rovnice), řekli jsme si, jak směrový vektor převést na normálový, řekli jsme si, jak vypočítat délku vektoru
příklady na procvičení:
a) jsou dány body A[4;7], B[3;12]; napište souřadnice vektoru u=B-A; napište parametrické vyjádření přímky procházející bodem A, se směrovým vektorem u
b) jsou dány body A[2;9], B[5;8]; napište souřadnice vektoru u=B-A; tento vektor - směrový vektor přímky převeďte na normálový vektor přímky n; napište obecnou rovnici přímky procházející bodem A, s normálovým vektorem n
c) jsou dány body A[8;-7], B[7;1]; napište souřadnice vektoru u=B-A; určete jeho velikost
1 hodina
příklady na procvičení (ze 4.10.2010 na 11.10.2010):
1a) přímka je dána rovnicí: 2x + 4y - 7 = 0; určete její normálový a směrový vektor
1b) přímka je dána rovnicí: -4x + 2y + 3 = 0; určete její normálový a směrový vektor
2a) určete obecnou rovnici přímky: p: x = 2 - 4t; y = 6 + 2t; t 
R
2b) určete obecnou rovnici přímky: q: x = 1 + t; y = - 6 - 5t; t R
3a) vypočítejte skalární součin vektorů u.v: u = (4; -2); v = (1; 5)
3b) vypočítejte skalární součin vektorů a.b: a = (-2; 7); b = (2; -3)
2 hodiny (11.10.2010)
test z učiva předchozích hodin; polohové a metrické úlohy
příklady na procvičení (z 11.10.2010 na 1.11.2010):
1) určete vzájemnou polohu dvou přímek (přímek p a q) daných zápisy:
p: 2x - 4y + 3 = 0; q: x = 2 - 3t; y = 1 + 2t; t R
pokud nepůjde o rovnoběžky, určete jejich průsečík a úhel, který svírají; v případě, že o rovnoběžky půjde, a půjde o rovnoběžky různé, určete vzdálenost těchto rovnoběžek
2) najděte patu kolmice spuštěné z bodu Q[8; -3] na přímku m: 5x + 2y - 6 = 0; určete vzdálenost bodu Q od přímky m
3) určete vzájemnou polohu dvou přímek (přímek r a s) daných zápisy:
r: x = 2 + t; y = 7 - 4t; t R; s: x = 1 - 2t; y = 2 + 8t; t R
pokud nepůjde o rovnoběžky, určete jejich průsečík a úhel, který svírají; v případě, že o rovnoběžky půjde, a půjde o rovnoběžky různé, určete vzdálenost těchto rovnoběžek
4) najděte patu kolmice spuštěné z bodu H[-7; -3] na přímku k: x = 4 - 2t; y = -2 + t; t R; určete vzdálenost bodu H od přímky k
2. Kombinatorika
... trocha opakování a maturity
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Vyzkoušejte tento odkaz - jde o freewarový (volně šiřitelný) program geometrického náčrtníku: http://www.geogebra.org/cms/cz
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