Diketahui titik F(1,2,−4), G(3,3,−6), dan H(1,−1,−4). Nilai kosinus dari sudut yang terbentuk antara FG dan GH adalah ...

Pertanyaan

Diketahui titik straight F left parenthesis 1 comma 2 comma negative 4 right parenthesis comma space straight G left parenthesis 3 comma 3 comma negative 6 right parenthesis comma dan straight H left parenthesis 1 comma negative 1 comma negative 4 right parenthesis. Nilai kosinus dari sudut yang terbentuk antara FG with rightwards arrow on top dan GH with rightwards arrow on top adalah ... 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

OF with rightwards arrow on top equals straight f with rightwards arrow on top equals open parentheses 1 comma 2 comma negative 4 close parentheses OG with rightwards arrow on top equals straight g with rightwards arrow on top equals open parentheses 3 comma 3 comma negative 6 close parentheses OH with rightwards arrow on top equals straight h with rightwards arrow on top equals open parentheses 1 comma negative 1 comma negative 4 close parentheses

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell FG with rightwards arrow on top end cell equals cell straight g with rightwards arrow on top minus straight f with rightwards arrow on top end cell row blank equals cell open parentheses 3 comma 3 comma negative 6 close parentheses minus open parentheses 1.2. negative 4 close parentheses end cell row blank equals cell open parentheses 2 comma 1 comma negative 2 close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar FG with rightwards arrow on top close vertical bar equals square root of 2 squared plus 1 squared plus open parentheses negative 2 close parentheses squared end root equals square root of 4 plus 1 plus 4 end root equals 3 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell GH with rightwards arrow on top end cell equals cell straight h with rightwards arrow on top minus straight g with rightwards arrow on top end cell row blank equals cell open parentheses 1 comma negative 1 comma negative 4 close parentheses minus open parentheses 3 comma 3 comma negative 6 close parentheses end cell row blank equals cell open parentheses negative 2 comma negative 4 comma 2 close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack G H with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 2 close parentheses squared plus open parentheses negative 4 close parentheses squared plus 2 squared end root end cell row blank equals cell square root of 4 plus 16 plus 4 end root end cell row blank equals cell square root of 24 end cell row blank equals cell 2 square root of 6 end cell end table

Nilai cos dari sudut yang terbentuk antara  FG with rightwards arrow on top dan GH with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight alpha end cell equals cell fraction numerator FG with rightwards arrow on top times GH with rightwards arrow on top over denominator open vertical bar FG with rightwards arrow on top close vertical bar open vertical bar GH with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses 2 comma 1 comma negative 2 close parentheses open parentheses negative 2 comma negative 4 comma 2 close parentheses over denominator 3 times 2 square root of 6 end fraction end cell row blank equals cell fraction numerator negative 4 minus 4 minus 4 over denominator 6 square root of 6 end fraction end cell row blank equals cell fraction numerator negative 12 over denominator 6 square root of 6 end fraction times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell negative 1 third square root of 6 end cell end table

Jadi, nilai cos dari sudut yang terbentuk antara  FG with rightwards arrow on top dan GH with rightwards arrow on top adalah bold minus bold 1 over bold 3 square root of bold 6

 

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Vektor posisi A, B, C, dan D relatif terhadap titik asal O masing-masing adalah (13​), (97​), (59​), dan (x2​). Tentukan nilai x sehingga AD sejajar CB.

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