vektor1[1]
DESCRIPTION
VEKTORTRANSCRIPT
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VEKTOR (1)IR. I NYOMAN SETIAWAN, MT
PS. TEKNIK ELEKTROUNIVERSITAS UDAYANA
E-mail :[email protected]@ee.unud.ac.id
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VektorBesaran fisis :1. Besaran Skalar : besaran yang cukup dinyatakan oleh
sebuah bilangan dengan satuannya yang sesuai2. Besaran Vektor : besaran yang dinyatakan oleh sebuah
bilangan dengan satuannya yang sesuai dan arahnya
Penggambaran VektorVektor adalah suatu segmen garis berarah
a B
AB
Ujung vektor
ATitik awal
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Kesamaan Vektor
Dua vektor dikatakan sama jika dan hanyajika kedua vektor itu mempunyai panjangsama dan arah sama
b = -aa = ba
b
a
b
Vektor yang mempunyai panjangsama tetapi dengan arah berbeda
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Komponen VektorP(x1,y1,z1)Q(x2,y2,z2)
[ ]321 ,, aaa=a
23
22
21 aaa ++=a
Panjang vektor a
12
12
12
zza
yyaxxa
z
y
x
−=
−=−=
123
122
121
zzayyaxxa
−=−=−=
atau
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Penjumlahan Vektor
bac +=[ ]332211 ,, bababa +++=+ba
0a)(aaa00a
w)(vuwv)(uabba
=−+=+=+
++=+++=+
.4
.3
.2.1
Sifat-sifat
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Perkalian Vektor denganSkalar
[ ]321 ,, aaa=a dan c bilangan, makaJika
[ ]321 ,, cacacac =a
Sifat-sifat
aaaa
aa)a(baba
==
+=++=+
1.4)()(.3
.2)(.1
ckkckckcccc
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Vektor-Vektor Satuan : i, j, k
[ ] kjia 321321 ,, aaaaaa ++==
[ ] [ ] [ ]1,0,0,0,1,0,0,0,1 === kji
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Cosinus Arah (Direction Cosines)
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Contoh :
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Sudut antara dua vektor
Contoh :
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Perkalian skalar antara duavektor (dot product)
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Contoh :
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Perkalian Vektor (perkaliansilang)
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Contoh :
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Contoh :
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Hasil Kali Tripel Skalar (Triple Product)
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Hasil Kali Tripel Skalar (Triple Product)
Contoh :