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Jika vektor a dan b mempunyai panjang yang sama dan vektor (a−2b) tegak lurus terhadap vektor , maka besar sudut antara dan adalah ....

Pertanyaan

Jika vektor italic a with rightwards arrow on top dan b with rightwards arrow on top mempunyai panjang yang sama dan vektor open parentheses a with rightwards arrow on top minus 2 b with rightwards arrow on top close parentheses tegak lurus terhadap vektor italic a with rightwards arrow on top, maka besar sudut antara italic a with rightwards arrow on top dan b with rightwards arrow on top adalah ....

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

 alpha equals 60 degree.

Pembahasan

Jika vektor italic a with rightwards arrow on top dan b with rightwards arrow on top mempunyai panjang yang sama dan vektor open parentheses a with rightwards arrow on top minus 2 b with rightwards arrow on top close parentheses tegak lurus terhadap vektor italic a with rightwards arrow on top, maka

open vertical bar italic a with rightwards arrow on top close vertical bar equals open vertical bar italic b with rightwards arrow on top close vertical bar

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a with rightwards arrow on top minus 2 b with rightwards arrow on top close parentheses times a with rightwards arrow on top end cell equals 0 row cell open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar a with rightwards arrow on top close vertical bar minus 2 times open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar b with rightwards arrow on top close vertical bar times cos space alpha end cell equals 0 row cell open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar a with rightwards arrow on top close vertical bar minus 2 times open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar a with rightwards arrow on top close vertical bar times cos space alpha end cell equals 0 row cell open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell 2 times open vertical bar a with rightwards arrow on top close vertical bar times open vertical bar a with rightwards arrow on top close vertical bar times cos space alpha end cell row 1 equals cell 2 times cos space alpha end cell row cell cos space alpha end cell equals cell 1 half end cell end table

Dengan demikian, diperoleh

italic a italic r italic c table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 60 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table

Jadi, alpha equals 60 degree.

277

4.2 (5 rating)

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Diberikan vektor sehingga ∣a∣=3, ∣b∣=23​. Jika sudut antara dua vektor tersebut adalah 30∘, maka nilai ∣a+b∣ adalah ....

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