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diketahui vektor a=⎝⎛​34−5​⎠⎞​ dan b=⎝⎛​1−22​⎠⎞​. Nilai sinus sudut antara adan b adalah...

Pertanyaan

d i k e t a h u i space v e k t o r space a with rightwards arrow on top equals open parentheses table row 3 row 4 row cell negative 5 end cell end table close parentheses space d a n space b with rightwards arrow on top equals open parentheses table row 1 row cell negative 2 end cell row 2 end table close parentheses. space N i l a i space sin u s space s u d u t space a n t a r a space a with rightwards arrow on top d a n space b with rightwards arrow on top space a d a l a h...

  1. negative 1 half square root of 3

  2. negative 1 half square root of 2

  3. negative 1 third square root of 3

  4. 1 half square root of 2

  5. 1 half square root of 3

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

vertical line a ⃗ vertical line equals square root of 3 squared plus 4 squared plus negative 5 squared right parenthesis end root equals square root of 9 plus 16 plus 25 end root equals square root of 50 equals 5 square root of 2  vertical line b ⃗ vertical line equals square root of 1 squared plus negative 2 squared plus 2 squared right parenthesis end root equals square root of 1 plus 4 plus 4 end root equals square root of 9 equals 3    a ⃗. b ⃗ equals vertical line a ⃗ vertical line. vertical line b ⃗ vertical line c o s space alpha    left parenthesis 3 cross times 1 right parenthesis plus left parenthesis 4 cross times left parenthesis negative 2 right parenthesis right parenthesis plus left parenthesis left parenthesis negative 5 right parenthesis cross times 2 right parenthesis equals 5 square root of 2 cross times 3 cross times c o s space alpha  space space space space space space space space space space space space space space space space space space minus 15 space space space space space space space space space space space space space space space space space space space space space space space space space space equals 15 square root of 2 space c o s space alpha space  c o s space alpha equals negative fraction numerator 1 over denominator square root of 2 end fraction. fraction numerator square root of 2 over denominator square root of 2 end fraction  equals negative 1 half square root of 2

Nilai sudut α yg memenuhi adalah 135o dan 215o ( kuadran II dan kuadran III)

Karena sudut antara 2 vektor kurang dari 180o maka α = 135o

sin = sin 135o = 

126

3.9 (11 rating)

izzah lailatul

Ini yang aku cari!

Sitti Rayyani

Jawaban tidak sesuai

Pertanyaan serupa

Hitunglah besar sudut antara vektor a=3i+2j​+4k dan b=2i+3j​+3k.

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