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Diketahui ∣ ∣ ​ a ∣ ∣ ​ = 1 , ∣ ∣ ​ b ∣ ∣ ​ = 4 dan a ⋅ b = 3 . Tentukan ∣ ∣ ​ a + b ∣ ∣ ​ !

Diketahui  dan . Tentukan 

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D. Rajib

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Mahasiswa/Alumni Universitas Muhammadiyah Malang

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.

 begin mathsize 14px style vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line equals square root of 23 end style.

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Jadi .

begin mathsize 14px style cos alpha equals fraction numerator a. b over denominator open vertical bar a with rightwards arrow on top close vertical bar. open vertical bar b with rightwards arrow on top close vertical bar end fraction space space space space space space space space space equals fraction numerator 3 over denominator 1.4 end fraction space space space space space space space space space equals 3 over 4 vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line equals 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 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar cos alpha end root space space space space space space space space space space equals square root of 1 squared plus 4 squared plus 2.1.4.3 over 4 end root space space space space space space space space space space equals square root of 1 plus 16 plus 6 end root space space space space space space space space space space equals square root of 23 end style 

Jadi begin mathsize 14px style vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line equals square root of 23 end style.

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