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Panjang vektor satuan dari vektor  .

Pertanyaan

Panjang vektor satuan dari vektor square root of 125 i with rightwards arrow on top plus root index 8 of 136 j with rightwards arrow on top minus square root of 144 k with rightwards arrow on top equals... .

  1. 1 

  2. 0 

  3. square root of 255 

  4. square root of 150 

  5. square root of 125 

Pembahasan Soal:

Diketahui vektor square root of 125 i with rightwards arrow on top plus root index 8 of 136 j with rightwards arrow on top minus square root of 144 k with rightwards arrow on top. Vektor satuan adalah vektor yang panjangnya 1 sehingga vektor satuan dari sembarang vektor panjangnya 1. Dengan demikian, panjang vektor satuan dari vektor  square root of 125 i with rightwards arrow on top plus root index 8 of 136 j with rightwards arrow on top minus square root of 144 k with rightwards arrow on top adalah 1.

Oleh karena itu, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Hajrianti

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 07 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan vektor satuan dari vektor-vektor berikut! b.  dengan  dan

Pembahasan Soal:

Vektor posisi dari titik begin mathsize 14px style straight M open parentheses 2 comma space 1 comma space 2 close parentheses end style dan Error converting from MathML to accessible text. adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell OM with rightwards arrow on top end cell equals cell open parentheses table row 2 row 1 row 2 end table close parentheses end cell row cell ON with rightwards arrow on top end cell equals cell open parentheses table row 2 row 0 row 3 end table close parentheses end cell end table end style 

Vektor begin mathsize 14px style MN with rightwards arrow on top end style dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell MN with rightwards arrow on top end cell equals cell ON with rightwards arrow on top minus OM with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row 0 row 3 end table close parentheses minus open parentheses table row 2 row 1 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 1 end cell row 1 end table close parentheses end cell end table end style 

Panjang vektor begin mathsize 14px style MN with rightwards arrow on top end style dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar MN with rightwards arrow on top close vertical bar end cell equals cell square root of 0 squared plus open parentheses negative 1 close parentheses squared plus 1 squared end root end cell row blank equals cell square root of 0 plus 1 plus 1 end root end cell row blank equals cell square root of 2 end cell end table end style 

Misalkan vektor satuan dari vektor begin mathsize 14px style MN with rightwards arrow on top end style adalah vektor begin mathsize 14px style a with rightwards arrow on top end style. Dengan menerapkan rumus vektor satuan, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell fraction numerator MN with rightwards arrow on top over denominator open vertical bar MN with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator open vertical bar MN with rightwards arrow on top close vertical bar end fraction MN with rightwards arrow on top end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction open parentheses table row 0 row cell negative 1 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative fraction numerator 1 over denominator square root of 2 end fraction end cell row cell fraction numerator 1 over denominator square root of 2 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell end table close parentheses end cell end table end style 

Jadi, vektor satuan dari vektor begin mathsize 14px style MN with rightwards arrow on top end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 0 row cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell end table close parentheses end cell end table end style.

0

Roboguru

Jika koordinat titik dan , maka tentukan koordinat titik !

Pembahasan Soal:

Ingat cara untuk menentukan suatu vektor dari 2 titik koordinat yaitu AB with rightwards arrow on top equals straight B minus straight A. Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row cell open parentheses table row 4 row cell negative 2 end cell row 5 end table close parentheses end cell equals cell straight B minus open parentheses table row cell negative 5 end cell row 4 row 1 end table close parentheses end cell row cell open parentheses table row 4 row cell negative 2 end cell row 5 end table close parentheses plus open parentheses table row cell negative 5 end cell row 4 row 1 end table close parentheses end cell equals straight B row cell open parentheses table row cell negative 1 end cell row 2 row 6 end table close parentheses end cell equals straight B end table

Jadi, dapat disimpulkan bahwa titik koordinat B adalah left parenthesis negative 1 comma 2 comma 6 right parenthesis.

0

Roboguru

Tentukan vektor satuan dari vektor-vektor berikut.

Pembahasan Soal:

Ingat konsep vektor satuan dari vektor tiga dimensi u with rightwards arrow on top equals open parentheses table row a row b row c end table close parentheses:

Vektor space satuan space u with rightwards arrow on top equals fraction numerator 1 over denominator square root of a squared plus b squared plus c squared end root end fraction open parentheses table row a row b row c end table close parentheses 

diketahui u with rightwards arrow on top equals open parentheses table row 0 row 0 row cell negative 1 end cell end table close parentheses maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell Vektor space satuan space u with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator square root of 0 squared plus 0 squared plus open parentheses negative 1 close parentheses squared end root end fraction open parentheses table row 0 row 0 row cell negative 1 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 1 end fraction open parentheses table row 0 row 0 row cell negative 1 end cell end table close parentheses end cell row blank equals cell 1 over 1 open parentheses table row 0 row 0 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row 0 row cell negative 1 end cell end table close parentheses end cell end table 

Dengan demikian vektor satuan dari vektor tersebut adalah open parentheses table row 0 row 0 row cell negative 1 end cell end table close parentheses.

0

Roboguru

Jika  adalah vektor satuan, maka t = ....

Pembahasan Soal:

Karena begin mathsize 14px style u with rightwards arrow on top equals 2 t i with rightwards arrow on top plus 6 t j with rightwards arrow on top plus 9 t k with rightwards arrow on top end style adalah vektor satuan, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar u with rightwards arrow on top close vertical bar end cell equals 1 row cell square root of open parentheses 2 t close parentheses squared plus open parentheses 6 t close parentheses squared plus open parentheses 9 t close parentheses squared end root end cell equals 1 row cell square root of 4 t squared plus 36 t squared plus 81 t squared end root end cell equals 1 row cell square root of 121 t squared end root end cell equals 1 row cell square root of 121 times square root of t squared end root end cell equals 1 end table end style

Ingat bahwa begin mathsize 14px style square root of x squared end root equals open vertical bar x close vertical bar end style, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 121 times square root of t squared end root end cell equals 1 row cell 11 open vertical bar t close vertical bar end cell equals 1 row cell open vertical bar t close vertical bar end cell equals cell 1 over 11 end cell row t equals cell 1 over 11 text  atau  end text t equals negative 1 over 11 end cell end table end style  

0

Roboguru

Vektor satuan dari vektor  adalah...

Pembahasan Soal:

Rumus vektor satuan :

a equals fraction numerator a with rightwards harpoon with barb upwards on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction

Maka, vektor satuan dari a with rightwards arrow on top equals open parentheses 2 comma 1 comma negative 2 close parentheses,

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell fraction numerator open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses over denominator square root of 2 squared plus 1 squared plus open parentheses negative 2 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses over denominator square root of 4 plus 1 plus 4 end root end fraction end cell row blank equals cell fraction numerator open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses over denominator square root of 9 end fraction end cell row blank equals cell fraction numerator open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses over denominator 3 end fraction end cell row blank equals cell open parentheses table row cell 2 over 3 end cell row cell 1 third end cell row cell negative 2 over 3 end cell end table close parentheses end cell row blank equals cell open parentheses 2 over 3 comma 1 third comma space minus 2 over 3 close parentheses end cell end table

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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