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Diketahui vektor x ⇀ = ( 6 4 ​ ) , y ⇀ ​ = ( 2 5 ​ ) , dan z ⇀ = ( − 1 3 ​ ) . Tentukan ∣ ∣ ​ xy ⇀ ​ ∣ ∣ ​ − ∣ ∣ ​ xz ⇀ ∣ ∣ ​ !

Diketahui vektor , , dan . Tentukan !

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai dari .

 nilai dari begin mathsize 14px style open vertical bar xy with rightwards harpoon with barb upwards on top close vertical bar minus open vertical bar xz with rightwards harpoon with barb upwards on top close vertical bar equals square root of 17 plus 5 square root of 2 end style.

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Pembahasan

, , dan , sehingga Jadi,nilai dari .

 begin mathsize 14px style straight x with rightwards harpoon with barb upwards on top equals open parentheses table row 6 row 4 end table close parentheses end style, begin mathsize 14px style straight y with rightwards harpoon with barb upwards on top equals open parentheses table row 2 row 5 end table close parentheses end style, dan begin mathsize 14px style straight z with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 1 end cell row 3 end table close parentheses end style, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar xy with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open parentheses 6 minus 2 close parentheses squared plus open parentheses 4 minus 5 close parentheses squared end root end cell row cell open vertical bar xy with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 4 squared plus open parentheses negative 1 close parentheses squared end root end cell row cell open vertical bar xy with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 16 plus 1 end root end cell row cell open vertical bar xy with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 17 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line xz with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of left parenthesis 6 minus open parentheses negative 1 close parentheses right parenthesis squared plus left parenthesis 4 minus 3 right parenthesis squared end root end cell row cell vertical line xz with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of 7 squared plus 1 squared end root end cell row cell vertical line xz with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of 49 plus 1 end root end cell row cell vertical line xz with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of 50 end cell row cell vertical line xz with rightwards harpoon with barb upwards on top vertical line end cell equals cell 5 square root of 2 end cell end table end style

Jadi, nilai dari begin mathsize 14px style open vertical bar xy with rightwards harpoon with barb upwards on top close vertical bar minus open vertical bar xz with rightwards harpoon with barb upwards on top close vertical bar equals square root of 17 plus 5 square root of 2 end style.

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