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8 Daring Matematika 10 September 2020 - XI.docx
1.
Daring Matematika 10
September 2020 XI TKJ SMK WALISONGO Catat materi dan kerjakan latihan soalnya! ๏ถ Materi 1. Vektor Pada Bidang Datar (๐น๐) A. Vektor satuan ( ๐ โ ) ๐ โ = ๐ โ |๐ โ| Contoh : 1. Tentukan vektor satuan dari ๐ โโ =[ โ3 4 ]! Jawab: ๐ โ = ๐ โโ |๐ โโ| == [ โ3 4 ] โ(โ3)2 +42 = [ โ3 4 ] โ9+16 = [ โ3 4 ] โ25 = [ โ3 4 ] 5 = [ โ 3 5 4 5 ] 2. Tentukan vektor satuan dari ๐ โ =[ 2 0 ]! Jawab: ๐ โ = ๐ โ |๐ โ| == [2 0 ] โ22+02 = [ 2 0 ] โ4+0 = [2 0 ] โ4 = [2 0 ] 2 = [ 2 2 0 2 ] = [ 1 0 ] B. Perkalian vektor dengan skalar Contoh: Diketahui ๐ โ = [ 2 โ4 ] ๐๐๐ ๐ โโ = [ 1 โ5 ] Tentukan ; 1. 2๐ โ 2. โ3๐ โโ Jawab: 1. 2๐ โ =2. [ 2 โ4 ] = [ 4 โ8 ] 2. โ3๐ โโ=(-3). [ 1 โ5 ] = [ โ3 15 ] C. Penjumalahan Vektor 1. Cara Segitiga 2. Cara Jajar genjang Contoh: Diketahui ๐ โ = [ 2 4 ] ๐๐๐ ๐ โโ = [ 1 โ5 ] , ๐๐๐๐: 1. ๐ โ + ๐ โโ =[ 2 4 ] + [ 1 โ5 ] = [ 3 โ1 ] 2. ๐ โโ + 2๐ โโ =[ 2 4 ] + 2. [ 1 โ5 ] = [ 2 4 ] + [ 2 โ10 ] = [ 4 โ6 ] D. Selisih/pengurangan Vektor Contoh: Diketahui ๐ โ = [ 2 4 ] ๐๐๐ ๐ โโ = [ 1 โ5 ] , ๐๐๐๐: 1. ๐ โ โ ๐ โโ =[ 2 4 ] โ [ 1 โ5 ] = [ 2 โ 1 4 โ (โ5) ] = [ 1 9 ] 2. ๐ โโ โ 2๐ โโ =[ 2 4 ] โ 2. [ 1 โ5 ] = [ 2 4 ] โ [ 2 โ10 ] = [ 0 14 ]
2.
2. Vektor Pada
Bangun Ruang (๐น๐) A. Vektor satuan ( ๐ โ ) ๐ โ = ๐ โ |๐ โ| Contoh : 1. Tentukan vektor satuan dari ๐ โโ =[ 0 3 โ4 ]! Jawab: ๐ โ = ๐ โโ |๐ โโ| == [ 0 3 โ4 ] โ02+32(โ4) 2 = [ 0 3 โ4 ] โ0+9+16 = [ 0 3 โ4 ] โ25 = [ 0 3 โ4 ] 5 = [ 0 5 3 5 โ 4 5] =[ 0 3 5 โ 4 5 ] 2. Tentukan vektor satuan dari ๐ โ =2๐ โ+ ๐ โ + ๐ โโ Jawab: ๐ โ =2๐ โ + ๐ โ + ๐ โโ=[ ๐ ๐ ๐ ] = [ 2 1 1 ], maka ๐ โ = ๐ โ |๐ โ| = [ 2 1 1 ] โ22 +12 +12 = [ 2 1 1 ] โ4+1+1 = [ 2 1 1 ] โ6 = [ 2 โ6 1 โ6 1 โ6] B. Perkalian vektor dengan skalar Contoh: Diketahui ๐ โ = [ 2 0 โ4 ] ๐๐๐ ๐ โโ = [ 1 8 โ5 ] Tentukan ; 1. 3๐ โ 2. โ2๐ โโ Jawab: 1. 3๐ โ =3. [ 2 0 โ4 ] = [ 6 0 โ12 ] 2. โ2๐ โโ=(-2). [ 1 8 โ5 ] = [ โ2 โ16 10 ] C. Penjumalahan Vektor Contoh: Diketahui ๐ โ = [ 2 4 3 ] ๐๐๐ ๐ โโ = [ 1 โ5 โ4 ] , ๐๐๐๐: 1. ๐ โ + ๐ โโ =[ 2 4 3 ] + [ 1 โ5 โ4 ] = [ 3 โ1 โ1 ] 2. 3๐ โโ + ๐ โโ =3. [ 2 4 3 ] + [ 1 โ5 โ4 ] = [ 6 12 9 ] + [ 1 โ5 โ4 ] = [ 7 7 5 ] D. Selisih/pengurangan Vektor Contoh: Diketahui ๐ โ = [ 2 4 1 ] ๐๐๐ ๐ โโ = [ 1 โ5 3 ] , ๐๐๐๐: 1. ๐ โ โ ๐ โโ =[ 2 4 1 ] โ [ 1 โ5 3 ] = [ 1 10 โ2 ] 2. ๐ โโ โ 2๐ โโ =[ 2 1 1 ] โ 2. [ 1 โ5 3 ] = [ 2 4 1 ] โ [ 2 โ10 6 ] = [ 0 14 โ5 ]
3.
E. Materi Tambahan Contoh; 1.
Tentukan vektor satuannya a. ๐ โ = 4๐ โโ ๐ โ + ๐ โโ b. ๐ โ = โ4๐ โโ 2๐ โโ c. ๐ โ = ๐ โ โ 5๐ โโ Jawab. a. ๐ โ = 4๐ โโ ๐ โ + ๐ โโ = [ ๐ ๐ ๐ ] = [ 4 โ1 1 ], maka ๐ โ = ๐ โ |๐ โ| = [ 4 โ1 1 ] โ42+(โ1)2 +12 = [ 4 โ1 1 ] โ16+1+1 = [ 4 โ1 1 ] โ18 = [ 4 โ18 โ 1 โ18 1 โ18 ] b. ๐ โ = โ4๐ โโ 2๐ โโ=[ ๐ ๐ ๐ ] = [ 0 โ4 โ2 ], maka ๐ โ = ๐ โ |๐ โ| = [ 0 โ4 โ2 ] โ02 +(โ4)2 +(โ2)2 = [ 0 โ4 โ2 ] โ0+16+4 = [ 0 โ4 โ2 ] โ20 = [ 0 โ20 โ 4 โ20 โ 2 โ20] = [ 0 โ 4 โ20 โ 2 โ20 ] c. ๐ โ = ๐ โ โ 5๐ โโ = [ ๐ ๐ ๐ ] = [ 1 0 โ5 ], maka ๐ โ = ๐ โ |๐ โโ| = [ 1 0 โ5 ] โ12 +02 +(โ5)2 = [ 1 0 โ5 ] โ1+0+25 = [ 1 0 โ5 ] โ26 = [ 1 โ26 0 โ26 โ 5 โ26] = [ 1 โ26 0 โ 5 โ26 ] ๏ถ Latihan Soal 1. Tentukan vektor satuannya a. ๐ โ =[ โ6 8 ] b. ๐ โโ = [ 0 4 ] c. ๐ โ = 3๐ โ + ๐ โ + ๐ โโ d. ๐ โ = ๐ โ โ ๐ โ + ๐ โโ e. ๐ โ = โ4๐ โ + 2๐ โโ ---Selamat mengerjakan---
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