Diketahui a=⎝⎛​0−4−4​⎠⎞​ dan b=⎝⎛​−40−4​⎠⎞​. Hitunglah besar sudut θ antara vektor a dan b.

Pertanyaan

Diketahui a with rightwards arrow on top equals open parentheses table row 0 row cell negative 4 end cell row cell negative 4 end cell end table close parentheses dan begin mathsize 14px style b with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 0 row cell negative 4 end cell end table close parentheses end style. Hitunglah besar sudut begin mathsize 14px style straight theta end style antara vektor a with rightwards arrow on top dan b with rightwards arrow on top.

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

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

Pembahasan

Ingat kembali:

begin mathsize 14px style cos space straight theta equals fraction numerator straight a with rightwards arrow on top times straight b with rightwards arrow on top over denominator stack open vertical bar straight a close vertical bar with rightwards arrow on top times open vertical bar straight b with rightwards arrow on top close vertical bar end fraction end style 

Diketahui:

begin mathsize 14px style straight a with rightwards arrow on top equals open parentheses table row 0 row cell negative 4 end cell row cell negative 4 end cell end table close parentheses end style dan begin mathsize 14px style b with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 0 row cell negative 4 end cell end table close parentheses end style.

Maka:

 begin mathsize 14px style cos space straight theta equals fraction numerator straight a with rightwards arrow on top times straight b with rightwards arrow on top over denominator stack vertical line straight a vertical line with rightwards arrow on top times vertical line straight b with rightwards arrow on top vertical line end fraction cos space straight theta equals fraction numerator open parentheses table row 0 row cell negative 4 end cell row cell negative 4 end cell end table close parentheses times open parentheses table row cell negative 4 end cell row 0 row cell negative 4 end cell end table close parentheses over denominator square root of 0 squared plus open parentheses negative 4 squared close parentheses plus open parentheses negative 4 close parentheses squared end root times square root of open parentheses negative 4 close parentheses squared plus 0 squared plus open parentheses negative 4 close parentheses squared end root end fraction cos space straight theta equals fraction numerator 0 plus 0 plus 16 over denominator square root of 0 plus 16 plus 16 end root times square root of 16 plus 0 plus 16 end root end fraction cos space straight theta equals fraction numerator 16 over denominator square root of 32 times square root of 32 end fraction cos space straight theta equals 16 over 32 cos space straight theta equals 1 half cos space straight theta equals cos space 60 degree space space space space space space straight theta equals 60 degree end style 

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

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