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Diketahui vektor a = i − 2 j ​ + 3 k dan vektor b = 3 i + j ​ + 2 k . Maka besar sudut antara dua vektor tersebut adalah ...

Diketahui vektor  dan vektor . Maka besar sudut antara dua vektor tersebut adalah ...

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A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

sudut antara adalah .

sudut antara begin mathsize 14px style straight a with rightwards arrow on top space dan space straight b with rightwards arrow on top end style adalah begin mathsize 14px style 60 degree end style.

Pembahasan

1.Menentukan 2. Menentukan 3. Menentukan 4. Menentukan tangensudut antara Jadi, sudut antara adalah .

1. Menentukan begin mathsize 14px style open vertical bar straight a with rightwards arrow on top close vertical bar end style

begin mathsize 14px style vertical line straight a with rightwards arrow on top vertical line equals square root of 1 squared plus left parenthesis negative 2 right parenthesis squared plus 3 to the power of 2 end exponent end root vertical line straight a with rightwards arrow on top vertical line equals square root of 1 plus 4 plus 9 end root vertical line straight a with rightwards arrow on top vertical line equals square root of 14 end style

2. Menentukan begin mathsize 14px style open vertical bar straight b with rightwards arrow on top close vertical bar end style

begin mathsize 14px style vertical line straight b with rightwards arrow on top vertical line equals square root of left parenthesis 3 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root vertical line straight b with rightwards arrow on top vertical line equals square root of 9 plus 1 plus 4 end root vertical line straight b with rightwards arrow on top vertical line equals square root of 14 end style

3. Menentukan begin mathsize 14px style straight a with rightwards arrow on top times straight b with rightwards arrow on top end style

begin mathsize 14px style straight a with rightwards arrow on top times straight b with rightwards arrow on top equals open parentheses table row 1 row cell negative 2 end cell row 3 end table close parentheses times open parentheses table row 3 row 1 row 2 end table close parentheses straight a with rightwards arrow on top times straight b with rightwards arrow on top equals 3 minus 2 plus 6 straight a with rightwards arrow on top times straight b with rightwards arrow on top equals 7 end style

4. Menentukan tangen sudut antara begin mathsize 14px style straight a with rightwards arrow on top space dan space straight b with rightwards arrow on top end style

begin mathsize 14px style cos space straight alpha equals fraction numerator straight a with rightwards arrow on top times straight b with rightwards arrow on top over denominator vertical line straight a with rightwards arrow on top vertical line vertical line straight b with rightwards arrow on top vertical line end fraction cos space straight alpha equals fraction numerator 7 over denominator vertical line square root of 14 vertical line vertical line square root of 14 vertical line end fraction cos space straight alpha equals 7 over 14 cos space straight alpha equals 1 half space space space space space space space straight alpha equals 60 degree end style

Jadi, sudut antara begin mathsize 14px style straight a with rightwards arrow on top space dan space straight b with rightwards arrow on top end style adalah begin mathsize 14px style 60 degree end style.

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