Page 48 - Modul Matematika Peminatan Kelas X KD 3.2 (Vektor)

Modul Matematika Peminatan Kelas X KD 3.2

⃗⃗⃗⃗⃗
d. dengan F (2 , 1 , 2) dan G (2 , 0 , 3) Pembilang dan
2 2 0 penyebut dikalikan
⃗⃗⃗⃗⃗ √2
= − = (0) − (1) = (−1)
3 2 1
⃗⃗⃗⃗⃗
2
2
| | = √0 + (−1) + 1 = √0 + 1 + 1 = √2
2
0
(−1) 0 0
⃗⃗⃗⃗⃗
1
⃗⃗⃗⃗⃗
Vektor satuan searah vektor = = 1 = 1 (−1) = (−√2)...5
⃗⃗⃗⃗⃗
| | √2 √2 2
1 √2
  2



4. . = 4


 1 

2
2

Panjang vektor = | | = √2 + 4 + 1 = √4 + 16 + 1 = √21 …………4
2
2
(4) 2 2√21
Vektor satuan searah vektor = = ⃗ = 1 = 1 (4) = 1 (4√21)…4

| ⃗ | √21 √21 21
1 √21
−1
⃗
⃗
⃗
. = − + 5 + = ( 5 )
1
2
2
2
⃗
⃗
⃗
⃗
Panjang = | | = √(−1) + 5 + 1 = √1 + 25 + 1 = √27 = 3√3………4
1
⃗
Vektor satuan searah vektor = = ⃗⃗ = − +5 + ⃗ = √3(− + 5 + )…4
⃗
⃗
| ⃗⃗ | 3√3 9
−3
⃗⃗⃗⃗⃗
. = ( 0 )
5
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
2
2
2
Panjang = | | = √(−3) + 0 + 5 = √9 + 0 + 25 = √44 = 2√11….4
−3
( 0 ) −3
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
Vektor satuan searah vektor = = = 5 = 1 √11 ( 0 )……………4
⃗⃗⃗⃗⃗
| | 2√11 22
5
⃗⃗⃗⃗⃗
5. Gambar vektor

……………..4

1 2 −1
⃗⃗⃗⃗⃗

a. = − = ( 3 ) − (−3) ( 6 )……………………………………………………………………2
−2 1 −3
⃗⃗⃗⃗⃗
2
2
2
| | = √(−1) + 6 +) − 3) = √1 + 36 + 9 = √46…………………………………………..2
−1 1
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
b. Vektor negatif dari = − = − ( 6 ) (−6)……………………………………………….2
−3 3

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