Pertanyaan

Vektor a dan b membentuk sudut α , dengan sin α = 7 1 . Jika ∣ ∣ a ∣ ∣ = 5 dan a . b = 30 maka b . b = ......

Vektor $a$ dan $b$ membentuk sudut $α$ , dengan $sin α = \frac{1}{7}$ . Jika $∣ ∣ a ∣ ∣ = 5$ dan $a . b = 30$ maka $b . b = ......$

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Maka didapat

$Perhatikan space bahwa sin space straight alpha equals fraction numerator 1 over denominator square root of 7 end fraction Menggunakan space perbandingan space segitiga space colon$

Maka didapat $cos space alpha equals fraction numerator square root of 6 over denominator square root of 7 end fraction$

$Maka space didapat space box enclose cos space straight alpha equals fraction numerator square root of 6 over denominator square root of 7 end fraction end enclose Ingat space bahwa straight a with rightwards arrow on top. straight b with rightwards arrow on top equals open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar cos space straight alpha square root of 30 equals square root of 5 open vertical bar straight b with rightwards arrow on top close vertical bar open parentheses fraction numerator square root of 6 over denominator square root of 7 end fraction close parentheses square root of 30 equals open parentheses fraction numerator square root of 30 over denominator square root of 7 end fraction close parentheses open vertical bar straight b with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar equals fraction numerator square root of 30 over denominator square root of 30 end fraction square root of 7 box enclose open vertical bar straight b with rightwards arrow on top close vertical bar equals square root of 7 end enclose Ingat space pula space bahwa straight b with rightwards arrow on top. straight b with rightwards arrow on top equals open vertical bar straight b with rightwards arrow on top close vertical bar squared equals open parentheses square root of 7 close parentheses squared equals box enclose 7$