mat104-bahar_odev4 - CALISMA SORULARI-4(2009-2010-Bahar...

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C ¸ ALIS ¸MA SORULARI-4 (2009-2010-Bahar) Dersin Adı: Mat104 Konu: Uzayda Vekt¨orler 1. v = 2 i - 4 j + 5 k ve u = - 2 i +4 j - 5 k vekt¨orleri verilsin. A¸ sa˘ gıda istenen ifadeleri hesaplayınız. (a) v · u , | v | , | u | , (b) v ve u arasındaki a¸cının kosin¨us¨u, (c) v nin u y¨on¨undeki skaler bile¸ seni, (d) proj v u . 2. K¨o¸ se noktaları A ( - 5 , 3) , B (1 , - 2) , C (6 , - 2) olan ¨u¸cgenin alanını hesaplayınız. 3. K¨o¸ se noktaları A ( - 1 , 2) , B (2 , 0) , C (7 , 1) , D (4 , 3) olan paralelkenarın alanını hesaplayınız. 4. K¨o¸ se noktaları A (3 , - 1 , 4) , B (1 , 2 , - 4) , C ( - 3 , 2 , 1) olan ABC ¨u¸ cgeninin a¸cılarını hesaplayınız. 5. u = 2 i - j + 3 k , v = - i + j + k , w = 3 i + 5 j - k vekt¨ orlerinin olu¸ sturdu˘gu kutunun hacmini hesaplayınız. 6. P ( - 2 , 0 , 3) ve Q (3 , 5 , - 2) noktalarından ge¸cen do˘grunun denklemini bulunuz. 7. x + y + z = 1 ve x + y = 2 d¨uzlemlerinin kesi¸ sti˘ gi do˘grunun parametrik denkelmlerini elde ediniz. 8. P (3 , 2 , 1) bir nokta ve x = 2 + 2 t , y = 1 + 6 t , z = 3 - t bir d¨uzlem olsun.
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