Pertanyaan

Diketahui vektor p = i + j − 4 k , d an q = − 2 i − j . Nilai sinus sudut antara vektor p dan q = ......

Diketahui vektor $p = i + j - 4 k, d an q = - 2 i - j .$ Nilai sinus sudut antara vektor $p$ dan $q$ = ......

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F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$Misalkan space straight alpha space adalah space sudut space antara space vektor space straight p with rightwards arrow on top space dan space straight q with rightwards arrow on top. Ingat space rumus space perkalian space titik space pada space vektor space colon straight p with rightwards arrow on top. straight q with rightwards arrow on top equals open vertical bar straight p with rightwards arrow on top close vertical bar open vertical bar straight q with rightwards arrow on top close vertical bar cosα open parentheses table row 1 row 1 row cell negative 4 end cell end table close parentheses. open parentheses table row cell negative 2 end cell row cell negative 1 end cell row 0 end table close parentheses equals square root of 1 squared plus 1 squared plus left parenthesis negative 4 right parenthesis squared end root square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus 0 squared end root cosα minus 2 minus 1 plus 0 equals square root of 18 square root of 5 cosα minus 3 equals square root of 90 cosα minus 3 equals 3 square root of 10 cosα Berarti comma space cosα equals fraction numerator negative 3 over denominator 3 square root of 10 end fraction equals negative fraction numerator 1 over denominator square root of 10 end fraction sinα equals square root of 1 minus cos squared straight alpha end root equals square root of 1 minus open parentheses negative fraction numerator 1 over denominator square root of 10 end fraction close parentheses squared end root equals square root of 1 minus 1 over 10 end root equals square root of 9 over 10 end root equals 3 over 10 square root of 10 bold Catatan bold thin space bold colon Karena space sudut space antara space dua space vektor space bernilai space 0 degree less or equal than straight alpha less or equal than 180 degree comma space maka sin space straight alpha space tidaklah space negatif.$