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Pertanyaan

Diketahui titik-titik A ( 4 , 2 ) , B ( − 5 , − 1 ) , dan C ( 3 , − 5 ) pada sistem koordinat Cartesius. Misalkan d ⇀ , e ⇀ , dan f ⇀ ​ adalah vektor-vektor yang berturut-turut mewakili ruas garisberarah A B ⇀ , BC ⇀ , dan A C ⇀ .Tentukan: a. ∣ ∣ ​ d ⇀ ∣ ∣ ​ , ∣ ∣ ​ e ⇀ ∣ ∣ ​ , dan ∣ ∣ ​ f ⇀ ​ ∣ ∣ ​

Diketahui titik-titik  pada sistem koordinat Cartesius. Misalkan  adalah vektor-vektor yang berturut-turut mewakili ruas garis berarah . Tentukan:

a.  

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

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 begin mathsize 14px style open vertical bar straight d with rightwards harpoon with barb upwards on top close vertical bar equals 3 square root of 10 comma space open vertical bar straight e with rightwards harpoon with barb upwards on top close vertical bar equals 4 square root of 5 comma space dan space open vertical bar straight f with rightwards harpoon with barb upwards on top close vertical bar equals 5 square root of 2 end style.

Pembahasan

Diketahui titik-titik , dan .Vektor adalah vektor-vektor yang berturut-turut mewakili ruas garisberarah , sehingga Jadi, .

Diketahui titik-titik begin mathsize 14px style straight A left parenthesis 4 comma 2 right parenthesis comma space straight B left parenthesis negative 5 comma negative 1 right parenthesis end style, dan begin mathsize 14px style straight C left parenthesis 3 comma negative 5 right parenthesis end style. Vektor begin mathsize 14px style d with rightwards harpoon with barb upwards on top comma space e with rightwards harpoon with barb upwards on top comma space dan space f with rightwards harpoon with barb upwards on top end style adalah vektor-vektor yang berturut-turut mewakili ruas garis berarah begin mathsize 14px style AB with rightwards harpoon with barb upwards on top comma space BC with rightwards harpoon with barb upwards on top comma space dan space AC with rightwards harpoon with barb upwards on top end style, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards harpoon with barb upwards on top end cell equals cell AB with rightwards harpoon with barb upwards on top end cell row blank equals cell straight B minus straight A end cell row blank equals cell open parentheses table row cell negative 5 end cell row cell negative 1 end cell end table close parentheses minus open parentheses table row 4 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 9 end cell row cell negative 3 end cell end table close parentheses end cell row cell open vertical bar straight d with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open parentheses negative 9 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 81 plus 9 end root end cell row blank equals cell square root of 90 end cell row blank equals cell 3 square root of 10 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight e with rightwards harpoon with barb upwards on top end cell equals cell BC with rightwards harpoon with barb upwards on top end cell row blank equals cell straight C minus straight B end cell row blank equals cell open parentheses table row 3 row cell negative 5 end cell end table close parentheses minus open parentheses table row cell negative 5 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 4 end cell end table close parentheses end cell row cell vertical line straight e with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of 8 squared plus left parenthesis negative 4 right parenthesis squared end root end cell row blank equals cell square root of 64 plus 16 end root end cell row blank equals cell square root of 80 end cell row blank equals cell 4 square root of 5 end cell end table end style 

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

Jadi, begin mathsize 14px style open vertical bar straight d with rightwards harpoon with barb upwards on top close vertical bar equals 3 square root of 10 comma space open vertical bar straight e with rightwards harpoon with barb upwards on top close vertical bar equals 4 square root of 5 comma space dan space open vertical bar straight f with rightwards harpoon with barb upwards on top close vertical bar equals 5 square root of 2 end style.

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