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POKOK BAHASAN 2 PERKALIAN TITIK DAN SILANG

POKOK BAHASAN 2 PERKALIAN TITIK DAN SILANG. SPB 2.3 HASIL KALI TRIPEL SPB 2.4 HIMPUNAN VEKTOR-VEKTOR RESIPROKAL Oleh Nurul Saila Senin , 24 Oktober 2011 Selasa , 25 Oktober 2011. HASIL KALI TRIPEL.

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POKOK BAHASAN 2 PERKALIAN TITIK DAN SILANG

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  1. POKOK BAHASAN 2 PERKALIAN TITIK DAN SILANG SPB 2.3 HASIL KALI TRIPEL SPB 2.4 HIMPUNAN VEKTOR-VEKTOR RESIPROKAL OlehNurulSaila Senin, 24 Oktober 2011 Selasa, 25 Oktober 2011

  2. HASIL KALI TRIPEL • Hasil kali titikdansilangdarivektor A, B dan C akanberupa: (A.B)C, A.(BxC) dan Ax(BxC) • Hasil kali A.(BxC) disebuthasil kali tripelskalar(hasil kali kotak) [ABC]. • Hasil kali Ax(BxC) disebuthasil kali tripelvektor. Hukum-hukumyang berlaku: • (A.B)C  A(B.C) • A.(BxC)=B.(CxA)=C.(AxB)=volume sebuahjajaran-genjangruangygmemilikisisi-sisi A, B dan C ataunegatifdari volume ini, sesuai dg apakah A, B dan C membentuksebuahsistemtangankananataukahtidak.

  3. Jika A = A1i +A2j+A3k, B = B1i +B2j+B3k dan C = C1i +C2j+C3k, maka: • Ax(BxC)  (AxB)XC

  4. latihan • Hitunglah (2i-3j).[(i+j-k)x(3i-k)]. • Buktikanbhw A.(BxC) = B.(CxA) = C.(AxB). • Buktikanbhw A.(BxC) = (AxB).C. • Buktikanbhw A.(AxC) = 0 • Buktikanbhw: A.BxC = 0 jhj A, B, C terletaksebidang. • Misalkan r1=x1i+y1j+z1k, r2=x2i+y2j+z2k dan r3=x3i+y3j+z3k adl vektor2 kedudukandarititik-titik P1(x1,y1,z1), P2(x2,y2,z2) dan P3(x3,y3,z3). Carilah pers. Bidangygmelaluiketigatitikitu.

  5. Carilah pers. Bidangygditentukanolehtitik-titik P1(2, -1, 1), P2(3, 2, -1), P3(-1, 3, 2).

  6. POKOK BAHASAN 2 PERKALIAN TITIK DAN SILANG SUB POKOK BAHASAN 2.4 HIMPUNAN VEKTOR-VEKTOR RESIPROKAL OlehNurulSaila Senin, 24 Oktober 2011 Selasa, 25 Oktober 2011

  7. Himpunanvektor-vektorResiprokal • Himpunanvektor-vektor a, b, c dan a’, b’, c’ disebuthimpunanatausistemvektor-vektorresiprokaljika: a.a’=b.b’=c.c’ = 1 a’.b=a’.c=b’.a=b’.c=c’.a=c’.b=0 • Himpunan-himpunan a, b, c dan a’, b’, c’ adalahhimpunanvektor-vektorresiprokaljikadanhanyajika:

  8. Contoh: • Carilahsuatuhimpunanvektor-vektorresiprokalterhadaphimpunanvektor 2i+3j-k, i-j-2k, -i+2j+2k.

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