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Diketahui p⇀​=6i−3j−2k, q⇀​=3i+2j−k. Jika γ adalah sudut antara p⇀​ dan q⇀​. Nilai dari tan γ=...

Pertanyaan

Diketahui p with rightwards harpoon with barb upwards on top equals 6 i minus 3 j minus 2 k comma space q with rightwards harpoon with barb upwards on top equals 3 i plus 2 j minus k. Jika gamma adalah sudut antara p with rightwards harpoon with barb upwards on top dan q with rightwards harpoon with barb upwards on top. Nilai dari tan space gamma equals... 

  1. 3 square root of 10 

  2. 2 square root of 10 

  3. square root of 10 

  4. 1 half square root of 10 

  5. 1 third square root of 10 

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 6 row cell negative 3 end cell row cell negative 2 end cell end table close parentheses comma space q with rightwards harpoon with barb upwards on top equals open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses end cell row cell p with rightwards harpoon with barb upwards on top times q with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 6 row cell negative 3 end cell row cell negative 2 end cell end table close parentheses times open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses 6 cross times 3 close parentheses plus open parentheses negative 3 cross times 2 close parentheses plus open parentheses negative 2 cross times open parentheses negative 1 close parentheses close parentheses end cell row blank equals cell 18 minus 6 plus 2 end cell row blank equals 14 row cell open vertical bar p with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 6 squared plus open parentheses negative 3 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 36 plus 9 plus 4 end root end cell row blank equals cell square root of 49 end cell row blank equals 7 row cell open vertical bar q with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 3 squared plus 2 squared plus open parentheses negative 1 close parentheses squared end root end cell row blank equals cell square root of 9 plus 4 plus 1 end root end cell row blank equals cell square root of 14 end cell row cell cos space gamma end cell equals cell fraction numerator p with rightwards harpoon with barb upwards on top times q with rightwards harpoon with barb upwards on top over denominator open vertical bar p with rightwards harpoon with barb upwards on top close vertical bar times open vertical bar q with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row blank equals cell fraction numerator 14 over denominator 7 square root of 14 end fraction end cell row blank equals cell fraction numerator 14 over denominator 7 square root of 14 end fraction cross times fraction numerator square root of 14 over denominator square root of 14 end fraction end cell row blank equals cell fraction numerator 14 over denominator 7 cross times 14 end fraction square root of 14 end cell row blank equals cell 1 over 7 square root of 14 end cell row gamma equals cell a r c cos open parentheses 1 over 7 square root of 14 close parentheses end cell row blank equals cell 57 comma 6884668 degree end cell row cell tan space gamma end cell equals cell tan space open parentheses 57 comma 6884668 degree close parentheses end cell row blank equals cell 1 comma 58113883 end cell row blank equals cell 1 half square root of 10 end cell end table 

Jadi, nilai tan space gamma equals 1 half square root of 10.

Oleh karena itu, jawaban yang benar adalah D.

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