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

Pertanyaan

Diberikan vektor sehingga open vertical bar a close vertical bar equals 3, open vertical bar b close vertical bar equals 2 square root of 3. Jika sudut antara dua vektor tersebut adalah 30 degree, maka nilai open vertical bar a plus b close vertical bar adalah ....

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

  nilai dari open vertical bar a plus b close vertical bar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 39 end cell end table.

Pembahasan

Diberikan dua vektor sehingga open vertical bar a close vertical bar equals 3 dan open vertical bar b close vertical bar equals 2 square root of 3. Sudut antara dua vektor tersebut adalah 30 degree, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator 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 end fraction end cell row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell 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 30 degree end cell row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell left parenthesis 3 right parenthesis open parentheses up diagonal strike 2 square root of 3 close parentheses open parentheses fraction numerator square root of 3 over denominator up diagonal strike 2 end fraction close parentheses end cell row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell 3 times 3 end cell row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals 9 end table 

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses squared end root end cell row blank equals cell square root of open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared plus 2 times a with rightwards arrow on top times b with rightwards arrow on top end root end cell row blank equals cell square root of 3 squared plus open parentheses 2 square root of 3 close parentheses squared plus 2 times 9 end root end cell row blank equals cell square root of 9 plus 12 plus 18 end root end cell row blank equals cell square root of 39 end cell end table 

Jadi,  nilai dari open vertical bar a plus b close vertical bar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 39 end cell end table.

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