# Quiz Vektor Matematika

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Erli
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QUIZ VEKTOR MATEMATIKA & PEMBAHASAN

• 1.

### Diketahui vektor a = 2i – 6j – 3k dan b = 4i + 2j – 4k . Panjang proyeksi vektor a pada b adalah…..

• A.

4/3

• B.

8/9

• C.

¾

• D.

3/8

• E.

8/36

A. 4/3
Explanation
Panjang masing-masing vektor, jika nanti diperlukan datanya:
|a|=√(2^2+(〖-6)〗^2+(-3)^2 )=√49=7
|b|=√(4^2+〖(2)〗^2+〖(-4)〗^2 )=√36=6
Proyeksi vektor a pada vektor b, namakan c:
|c|=(a.b)/|b|
|c|=((2i-6j-3k)(4i+2j-2k))/6
|c|=(8-12+12)/6=4/3

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• 2.

### Diberikan tiga buah vektor masing-masing:a = 6p i + 2p j − 8 kb = −4 i + 8j + 10 kc = − 2 i + 3 j − 5 kJika vektor a tegak lurus b, maka vektor a − c adalah....

• A.

− 58 i − 20 j − 3k

• B.

− 58 i − 23 j − 3k

• C.

− 62 i − 17 j − 3k

• D.

− 62 i − 20 j − 3k

• E.

− 62 i − 23 j − 3k

B. − 58 i − 23 j − 3k
Explanation

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• 3.

### Ditentukan A(4 , 7 , 0) , B(6 , 10 , –6) dan C(1 , 9 , 0). AB dan AC wakil-wakil dari vektor u dan v. Besar sudut antara u dan v adalah....

• A.

0

• B.

1/4 π

• C.

π

• D.

3/4 π

• E.

1/2 π

E. 1/2 π
Explanation
Tentukan vektor u dan v terlebih dulu:
u = AB = B − A = (6 , 10 , –6) − (4 , 7 , 0) = (2, 3, −6) → u = 2i + 3j − 6k
v = AC = C − A = (1 , 9 , 0) − (4 , 7 , 0) = (− 3, 2, 0) → v = − 3i + 2j
cos∝=(u.v)/|u||v| =(-6+6+0)/(√49 √12)=0
Sudut dengan nilai cosinus nol adalah 90° atau 1/2 π

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• 4.

### Diketahui segitiga ABC dengan A(2, 1, 2), B(6, 1, 2), dan C(6, 5, 2). Jika vektor u mewakili vektor AB dan vektor v mewakili vektor AC, maka sudut yang dibentuk oleh vektor u dan v adalah…

• A.

30°

• B.

45°

• C.

60°

• D.

90°

• E.

120°

B. 45°
Explanation

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• 5.

### Nilai p agar vektor pi + 2j -6k dan 4i - 3j + k saling tegak lurus adalah....

• A.

-3

• B.

-2

• C.

-1

• D.

2

• E.

3

E. 3
Explanation

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• Current Version
• Mar 21, 2023
Quiz Edited by
ProProfs Editorial Team
• Dec 13, 2015
Quiz Created by
Erli