Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
ÊݹÇñÝ»ñ, ³é³ç³¹ñ³ÝùÝ»ñ, ѳñó»ñ<br />
1. ¸Çóáõù A(0; 0; 1), B(3; 0; 2), C(−1; −1; −1), D(4; −3; 0)£ ï»ù Ñ»ï¨Û³É<br />
»ñÏáõ í»ÏïáñÝ»ñÇ Ïááñ¹ÇݳïÝ»ñÁª !A#B + !C#D ¨ !A#B + 2!B#C + 3!C#D + 4!D#A£<br />
2. гÛïÝÇ »Ý ABCA 1 B 1 C 1 åñǽٳÛÇ ãáñë ·³·³ÃÝ»ñÇ Ïááñ¹ÇݳïÝ»ñÁª<br />
A (0; 0; 1), B(2; 1; 1), A 1 (3; 0; −2), C 1 (2; 2; −1)£<br />
ï»ù Ùݳó³Í »ñÏáõ ·³·³ÃÝ»ñÇ Ïááñ¹ÇݳïÝ»ñÁ£<br />
3. гÛïÝÇ »Ý ABCDA 1 B 1 C 1 D 1 ½áõ·³Ñ»é³ÝÇëïÇ ãáñë ·³·³ÃÝ»ñÇ Ïááñ-<br />
¹ÇݳïÝ»ñÁª<br />
³) A(1; 0; −1), B(2; −1; 1), C(3; 0; 0), C 1 (1; 2; 2),<br />
μ) A(−2; 1; 0), C(0; 1; 2), B 1 (−3; 1; 0), D 1 (−3; 0; 2)£<br />
ï»ù Ùݳó³Í ãáñë ·³·³ÃÝ»ñÇ Ïááñ¹ÇݳïÝ»ñÁ<br />
4. ܳËáñ¹ ËݹñÇ Ûáõñ³ù³ÝãÛáõñ ³) ¨ μ) »ÝóϻïÇ Ñ³Ù³ñ ·ïÝ»É<br />
!A#B + !C#D, !A#A 1 + !B#B 1 , !A#B + !B#C 1 + !C#D 1 + !D#A 1 í»ÏïáñÝ»ñÇ Ïááñ¹Çݳï-<br />
Ý»ñÁ£<br />
5. #a(1; 2; 3) í»ÏïáñÁ Ý»ñϳ۳óñ»ù #m(1; 1; 0), #n(1; 0; 1), #p(0; 1; 1) í»ÏïáñÝ»ñáí£<br />
6. îí³Í ¿ ABCDA 1 B 1 C 1 D 1 ½áõ·³Ñ»é³ÝÇëïÁ£<br />
³) ²ñï³Ñ³Ûï»ù !A#B 1 , !B#D 1 , !C#A 1 , !D#B 1 í»ÏïáñÝ»ñÁ !A#B 1 , !A#D ¨ !A#A 1 -áí£<br />
μ) ²ñï³Ñ³Ûï»ù !A#B 1 , !A#D ¨ !A#A 1 í»ÏïáñÝ»ñÁ !A#C 1 , !B#D 1 ¨ !C#A 1 -áí£<br />
·) ²ñï³Ñ³Ûï»ù !A#C 1 , !A#D ¨ !A#A 1 í»ÏïáñÝ»ñÁ !A#B 1 , !A#D 1 ¨ !A#C-áí£<br />
6.10 ì»ÏïáñÝ»ñÇ ëϳÉÛ³ñ ³ñï³¹ñÛ³ÉÁ<br />
ÐÇß»óÝ»Ýù ѳñóã³÷áõÃÛ³Ý ¹³ëÁÝóóáõÙ ïñí³Í »ñÏáõ í»ÏïáñÝ»ñÇ<br />
ëϳÉÛ³ñ ³ñï³¹ñÛ³ÉÇ ë³ÑÙ³ÝáõÙÁ£<br />
¸Çóáõù #a-Ý ¨ #b-Ý »ñÏáõ í»ÏïáñÝ»ñ »Ý, ϕ Ýñ³Ýóáí ϳ½Ùí³Í ³ÝÏÛáõÝÝ ¿£<br />
²Û¹ ¹»åùáõÙª<br />
#a ·#b = |#a| · |#b| = cos ϕ<br />
²Ûëï»Õ #a ·#b-Ý #a ¨ #b í»ÏïáñÝ»ñÇ ëϳÉÛ³ñ ³ñï³¹ñÛ³ÉÝ ¿£<br />
²Ûë ë³ÑÙ³ÝáõÙÁ å³Ñå³ÝíáõÙ ¿ ݳ¨ ï³ñ³ÍáõÃÛ³Ý #a ¨ #b í»ÏïáñÝ»ñÇ<br />
ѳٳñ£<br />
êϳÉÛ³ñ ³ñï³¹ñÛ³ÉÇ ë³ÑÙ³ÝáõÙÇó Ñ»ï¨áõÙ ¿ ÙÇ ß³ï ϳñ¨áñ ѳïÏáõ-<br />
ÃÛáõÝ, áñÁ Ñ³×³Ë û·ï³·áñÍíáõÙ ¿ ï³ñμ»ñ ËݹÇñÝ»ñÇ ÉáõÍÙ³Ý Å³Ù³Ý³Ï.<br />
65
Change language