Roboguru

Jika panjang vektor  berturut-turut  maka besar sudut antara  adalah ....

Pertanyaan

Jika panjang vektor u with rightwards arrow on top comma space v with rightwards arrow on top comma space dan space open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses berturut-turut 12 comma space 8 comma space dan space 4 square root of 7 maka besar sudut antara italic u with rightwards arrow on top space dan space italic v with rightwards arrow on top adalah ....

  1. 45 degree 

  2. 60 degree 

  3. 90 degree 

  4. 120 degree 

  5. 150 degree 

Pembahasan Soal:

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar u with rightwards arrow on top close vertical bar end cell equals 12 row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals 8 row cell open vertical bar u with rightwards arrow on top plus v with rightwards arrow on top close vertical bar end cell equals cell 4 square root of 7 end cell end table 

Sehingga dapat ditentukan:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar u with rightwards arrow on top plus v with rightwards arrow on top close vertical bar end cell equals cell square root of open vertical bar u with rightwards arrow on top close vertical bar squared plus open vertical bar v with rightwards arrow on top close vertical bar squared plus 2 open vertical bar u with rightwards arrow on top close vertical bar open vertical bar v with rightwards arrow on top close vertical bar space cos space theta end root end cell row cell 4 square root of 7 end cell equals cell square root of 12 squared plus 8 squared plus 2 times 12 times 8 times cos space theta end root end cell row cell open parentheses 4 square root of 7 close parentheses squared end cell equals cell 144 plus 64 plus 192 space cos space theta end cell row 112 equals cell 208 plus 192 space cos space theta end cell row cell cos space theta end cell equals cell fraction numerator 112 minus 208 over denominator 192 end fraction end cell row blank equals cell fraction numerator negative 96 over denominator 192 end fraction end cell row blank equals cell negative 1 half end cell row theta equals cell cos to the power of negative 1 end exponent open parentheses negative 1 half close parentheses end cell row blank equals cell 120 degree end cell end table 

Jadi, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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