Diketahui |p| = 5 dan |q| = 6. Jika <(p, q) = 30°, tentukan hasil dari:
a. p · (p + q)
b. p · (p - q)
a. p · (p + q) = p · p + p · q
= |p| |p| cos 0° + |p| |q| cos 30°
= 5 · 5 · 1 + 5 · 6 · ½√3
= 25 + 15√3
= 5 (5 + 3√3)
b. p · (p - q) = p · p - p · q
= |p| |p| cos 0° - |p| |q| cos 30°
= 5 · 5 · 1 - 5 · 6 · ½√3
= 25 - 15√3
= 5 (5 - 3√3)
_______________________
Mapel: Matematika
Kelas: X
Materi: Bab 7.1 - Vektor
Kata Kunci: Vektor, Panjang Vektor, Perkalian Dot
Kode Soal: 2
Kode Kategorisasi: 10.2.7.1 [Kelas 10 Matematika Bab 7.1 - Vektor]
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Verified answer
Diketahui |p| = 5 dan |q| = 6. Jika <(p, q) = 30°, tentukan hasil dari:
a. p · (p + q)
b. p · (p - q)
PEMBAHASAN
a. p · (p + q) = p · p + p · q
= |p| |p| cos 0° + |p| |q| cos 30°
= 5 · 5 · 1 + 5 · 6 · ½√3
= 25 + 15√3
= 5 (5 + 3√3)
b. p · (p - q) = p · p - p · q
= |p| |p| cos 0° - |p| |q| cos 30°
= 5 · 5 · 1 - 5 · 6 · ½√3
= 25 - 15√3
= 5 (5 - 3√3)
_______________________
Mapel: Matematika
Kelas: X
Materi: Bab 7.1 - Vektor
Kata Kunci: Vektor, Panjang Vektor, Perkalian Dot
Kode Soal: 2
Kode Kategorisasi: 10.2.7.1 [Kelas 10 Matematika Bab 7.1 - Vektor]