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Pertanyaan

Diketahui vektor a = ( 6 2 ​ ) dan b = ( − 3 9 ​ ) .Hitunglah a ⋅ b , ∣ ∣ ​ a ∣ ∣ ​ , dan ∣ ∣ ​ b ∣ ∣ ​ !

Diketahui vektor dan . Hitunglah , dan !

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh nilai dari a ⋅ b = 0 , ∣ ∣ ​ a ∣ ∣ ​ = 2 10 ​ dan ∣ ∣ ​ b ∣ ∣ ​ ​ = ​ 3 10 ​ ​ .

diperoleh nilai dari  dan .

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Pembahasan

Ingat. Diketahui vektor a = ( x y ​ ) dan b = ( m n ​ ) maka a ⋅ b = ( x y ​ ) ⋅ ( m n ​ ) = x m − y n Panjang a = x 2 + y 2 ​ Dot product dari adalah besar vektor besar vektor Jadi diperoleh nilai dari a ⋅ b = 0 , ∣ ∣ ​ a ∣ ∣ ​ = 2 10 ​ dan ∣ ∣ ​ b ∣ ∣ ​ ​ = ​ 3 10 ​ ​ .

Ingat. 

Diketahui vektor  dan  maka

  • Panjang   

Dot product dari begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top end style adalah

begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top equals open parentheses table row 6 row 2 end table close parentheses times open parentheses table row cell negative 3 end cell row 9 end table close parentheses equals negative 18 plus 18 equals 0 end style 

besar vektor begin mathsize 14px style a with rightwards arrow on top end style 

begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of 6 squared plus 2 squared end root space space space space space space equals square root of 36 plus 4 end root space space space space space space equals square root of 40 space space space space space space equals 2 square root of 10 end style 

besar vektor begin mathsize 14px style b with rightwards arrow on top end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 3 close parentheses squared plus 9 squared end root end cell row cell space space space space space space end cell equals cell square root of 9 plus 81 end root end cell row cell space space space space space space end cell equals cell square root of 90 end cell row cell space space space space space space end cell equals cell 3 square root of 10 end cell end table end style 

Jadi diperoleh nilai dari  dan .

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

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Diketahui 3 buah vektor yaitu: a b c ​ = = = ​ − 8 i + 4 j ​ 3 i + 8 j ​ 4 i − y j ​ ​ Jika a ⋅ b = ∣ ∣ ​ c ∣ ∣ ​ , maka tentukan nilai y .

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