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Pertanyaan

Diketahui a = ⎝ ⎛ ​ 2 0 − 2 ​ ⎠ ⎞ ​ dan b = ⎝ ⎛ ​ 4 0 − 4 ​ ⎠ ⎞ ​ membentuk sudut 6 0 ∘ . Hitunglah nilai a ⋅ b !

Diketahui  dan  membentuk sudut . Hitunglah nilai 

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai adalah .

 nilai begin mathsize 14px style straight a with rightwards arrow on top times straight b with rightwards arrow on top end style adalah begin mathsize 14px style 8 end style.

Pembahasan

Ingat kembali: Diketahui: Maka: Dengan demikian,nilai adalah .

Ingat kembali:

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

Diketahui:

begin mathsize 14px style straight a with rightwards arrow on top equals open parentheses table row 2 row 0 row cell negative 2 end cell end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row 4 row 0 row cell negative 4 end cell end table close parentheses comma space straight theta equals 60 degree end style 

Maka:

begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals open vertical bar straight a with rightwards arrow on top close vertical bar times space open vertical bar straight b with rightwards arrow on top close vertical bar times space cos space straight theta straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals square root of 2 squared plus 0 squared plus open parentheses negative 2 close parentheses squared end root times space square root of 4 squared plus 0 squared plus open parentheses negative 4 close parentheses squared end root times space cos space 60 degree straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals square root of 4 plus 0 plus 4 end root times space square root of 16 plus 0 plus 16 end root times space 1 half straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals square root of 8 times space square root of 32 times space 1 half straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals square root of 256 times space space 1 half straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals 16 times space 1 half straight a with rightwards harpoon with barb upwards on top times space straight b with rightwards arrow on top equals 8 end style 

Dengan demikian, nilai begin mathsize 14px style straight a with rightwards arrow on top times straight b with rightwards arrow on top end style adalah begin mathsize 14px style 8 end style.

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