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Hitunglah Vektor satuan dari Vektor u=(−6,8)

Pertanyaan

Hitunglah Vektor satuan dari Vektor u with rightwards arrow on top equals left parenthesis negative 6 comma 8 right parenthesis

  1. ....

  2. ....

Pembahasan Soal:

Vektor satuan : table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top end cell equals cell fraction numerator left parenthesis negative 6 comma 8 right parenthesis over denominator square root of left parenthesis negative 6 right parenthesis squared plus 8 to the power of 2 end exponent end root end fraction end cell row blank equals cell fraction numerator left parenthesis negative 6 comma 8 right parenthesis over denominator square root of 36 plus 64 end root end fraction end cell row blank equals cell fraction numerator left parenthesis negative 6 comma 8 right parenthesis over denominator square root of 100 end fraction end cell row blank equals cell fraction numerator left parenthesis negative 6 comma 8 right parenthesis over denominator 10 end fraction end cell row blank equals cell open parentheses fraction numerator negative 3 over denominator 5 end fraction comma 4 over 5 close parentheses end cell end table

Jadi, vektor satuan u with rightwards arrow on top equals open parentheses fraction numerator negative 3 over denominator 5 end fraction comma 4 over 5 close parentheses.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Indah

Mahasiswa/Alumni Universitas Lampung

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Vektor satuan dari vektor posisi A(8,15) adalah...

Pembahasan Soal:

Diketahui vektor posisi titik A ditulis top enclose O A end enclose equals left parenthesis 8 comma 15 right parenthesis.

table attributes columnalign right center left columnspacing 0px end attributes row cell Vektor space satuan space top enclose O A end enclose space end cell equals cell fraction numerator 1 over denominator open vertical bar top enclose O A end enclose close vertical bar end fraction times top enclose O A end enclose end cell row blank equals cell fraction numerator 1 over denominator square root of 8 squared plus 15 squared end root end fraction open parentheses table row 8 row 15 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 64 plus 225 end root end fraction open parentheses table row 8 row 15 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 289 end fraction open parentheses table row 8 row 15 end table close parentheses end cell row blank equals cell 1 over 17 open parentheses table row 8 row 15 end table close parentheses end cell end table

0

Roboguru

Misalkan vektor a⇀=(−3x​). Tentukan nilai x yang mungkin jika vektor satuan dari vektor a⇀ adalah (5−3​5x​​).

Pembahasan Soal:

Vektor satuan.

Diketahui:

vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 3 end cell row straight x end table close parentheses end style

maka

vektor satuan begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals fraction numerator straight a with rightwards harpoon with barb upwards on top over denominator open vertical bar straight a with rightwards harpoon with barb upwards on top close vertical bar end fraction end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end cell equals cell fraction numerator open parentheses table row cell negative 3 end cell row straight x end table close parentheses over denominator square root of left parenthesis negative 3 right parenthesis squared plus straight x to the power of 2 end exponent end root end fraction end cell row cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end cell equals cell fraction numerator open parentheses table row cell negative 3 end cell row straight x end table close parentheses over denominator square root of 9 plus straight x squared end root end fraction end cell row cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end cell equals cell open parentheses table row cell fraction numerator negative 3 over denominator square root of 9 plus straight x squared end root end fraction end cell row cell fraction numerator straight x over denominator square root of 9 plus straight x squared end root end fraction end cell end table close parentheses end cell row blank blank blank end table end style 

Dari kesamaan 2 vektor sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 9 plus straight x squared end root end cell equals 5 row cell 9 plus straight x squared end cell equals 25 row cell straight x squared end cell equals cell 25 minus 9 end cell row cell straight x squared end cell equals 16 row straight x equals cell plus-or-minus square root of 16 end cell row blank equals cell plus-or-minus 4 end cell end table end style 

Jadi, Jika vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 3 end cell row straight x end table close parentheses end style maka nilai begin mathsize 14px style x end style yang mungkin jika vektor satuan dari vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals end style begin mathsize 14px style open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end style adalah begin mathsize 14px style straight x equals plus-or-minus 4. end style 

0

Roboguru

Diketahui vector a=4i−3j maka vector satuan a adalah ...

Pembahasan Soal:

Langkah pertama untuk menyelesaikan soal di atas adalah dengan menentukan panjang vektor a.

Seperti yang kamu ketahui, kuadrat panjang vektor a sama dengan jumlah kuadrat komponen-komponennya.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight a close vertical bar squared end cell equals cell 4 squared plus open parentheses negative 3 close parentheses squared end cell row blank equals cell 16 plus 9 end cell row blank equals 25 row blank equals cell square root of 25 end cell row blank equals cell plus-or-minus 5 end cell end table

Karena panjang tidak pernah negatif, maka nilai a = 5

Langkah kedua adalah menentukan vektor satuan yang searah dengan vektor a, yaitu fraction numerator a over denominator open vertical bar a close vertical bar end fraction.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight a over denominator open vertical bar straight a close vertical bar end fraction end cell equals cell fraction numerator 4 straight i minus 3 straight j over denominator 5 end fraction end cell row blank equals cell 4 over 5 straight i minus 3 over 5 straight j end cell end table

Jadi, dapat disimpulkan bahwa vektor satuan yang mempunyai arah sama dengan vektor straight a equals 4 straight i minus 3 straight j adalah vektor adalah 4 over 5 straight i space minus 3 over 5 straight j.

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Roboguru

Diketahui vektor , , dan . Vektor satuan yang searah dengan a−2b+c adalah ....

Pembahasan Soal:

Maka begin mathsize 14px style d with rightwards arrow on top equals a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end style. Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell d with rightwards arrow on top end cell equals cell a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end cell row blank equals cell open parentheses table row 3 row 0 end table close parentheses minus 2 open parentheses table row cell negative 2 end cell row 5 end table close parentheses plus open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 0 end table close parentheses minus open parentheses table row cell negative 4 end cell row 10 end table close parentheses plus open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 minus open parentheses negative 4 close parentheses plus open parentheses negative 1 close parentheses end cell row cell 0 minus 10 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 6 end cell end table close parentheses end cell end table end style

Kemudian didapat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar d with rightwards arrow on top close vertical bar end cell equals cell square root of 6 squared plus open parentheses negative 6 close parentheses squared end root end cell row blank equals cell square root of 36 plus 36 end root end cell row blank equals cell square root of 72 end cell row blank equals cell 6 square root of 2 end cell end table end style

Sehingga vektor satuan yang searah dengan begin mathsize 14px style d with rightwards arrow on top equals a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end style adalah

begin mathsize 14px style e subscript d with rightwards arrow on top end subscript equals fraction numerator d with rightwards arrow on top over denominator open vertical bar d with rightwards arrow on top close vertical bar end fraction equals fraction numerator 1 over denominator 6 square root of 2 end fraction open parentheses table row 6 row cell negative 6 end cell end table close parentheses equals open parentheses table row cell fraction numerator 6 over denominator 6 square root of 2 end fraction end cell row cell negative fraction numerator 6 over denominator 6 square root of 2 end fraction end cell end table close parentheses equals open parentheses table row cell fraction numerator 1 over denominator square root of 2 end fraction end cell row cell negative fraction numerator 1 over denominator square root of 2 end fraction end cell end table close parentheses equals open parentheses table row cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell end table close parentheses end style  

0

Roboguru

Diketahui titik O titik pangkal, dan titik-titik A,B,danC dengan vektor posisi OA=9i−10j​,OB=4i+2j​, dan OC=mi−2j​. a.  Tentukan vektor satuan yang searah AB

Pembahasan Soal:

Vektor begin mathsize 14px style stack A B with rightwards arrow on top end style didapakan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row blank equals cell open parentheses table row 4 row 2 end table close parentheses minus open parentheses table row 9 row cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell row 12 end table close parentheses end cell end table end style 

Vektor satuan yang searah begin mathsize 14px style stack A B with rightwards arrow on top end style didapatkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Vektor space satuan space stack A B with rightwards arrow on top end cell equals cell fraction numerator stack A B with rightwards arrow on top over denominator open vertical bar stack A B with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator square root of open parentheses negative 5 close parentheses squared plus 12 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator square root of 25 plus 144 end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator square root of 169 end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator 13 end fraction end cell row blank equals cell open parentheses table row cell negative 5 over 13 end cell row cell 12 over 13 end cell end table close parentheses end cell end table end style 

Dengan demikian, vektor satuan yang searah begin mathsize 14px style stack A B with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row cell negative 5 over 13 end cell row cell 12 over 13 end cell end table close parentheses end style.

0

Roboguru

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