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Diketahui vektor  dan modulus besar vektor . Nilai adalah ...

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals x i with rightwards arrow on top minus 8 j with rightwards arrow on top dan modulus besar vektor open vertical bar a with rightwards arrow on top close vertical bar equals 10. Nilai x adalah ...

  1. negative 5 atau 5

  2. 5 atau 6

  3. negative 5 atau negative 6

  4. negative 5 atau 6

  5. negative 6 atau 6

Pembahasan Soal:

Ingat rumus untuk menentukan panjang suatu vektor pada dimensi dua, dengan menggunakan rumus itu nantinya nilai x akan diketahui.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared end root end cell row 10 equals cell square root of x squared plus left parenthesis negative 8 right parenthesis squared end root end cell row 10 equals cell square root of x squared plus 64 end root end cell row cell 10 squared end cell equals cell x squared plus 64 end cell row 100 equals cell x squared plus 64 end cell row cell 100 minus 64 end cell equals cell x squared end cell row 36 equals cell x squared end cell row cell square root of 36 end cell equals x row cell plus-or-minus 6 end cell equals x end table

Jadi, dapat disimpulkan bahwa nilai x yang memenuhi adalah 6 atau negative 6.

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Panjang vektor  adalah ....

Pembahasan Soal:

Jika begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses end style, maka panjang vektor begin mathsize 14px style a with rightwards arrow on top equals open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root end style.

undefined, maka panjang vektor begin mathsize 14px style v 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 v with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 4 right parenthesis squared plus 6 to the power of 2 end exponent end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell square root of 4 times 13 end root end cell row blank equals cell 2 square root of 13 end cell row blank blank blank end table end style
 

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Panjang vektor  adalah ....

Pembahasan Soal:

Jika begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses end style, maka panjang vektornya adalah begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root end style.

begin mathsize 14px style v with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 6 end table close parentheses end style, panjang vektornya:
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 4 right parenthesis squared plus 6 to the power of 2 end exponent end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell 2 square root of 13 end cell end table end style
 

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Panjang vektor  adalah ....

Pembahasan Soal:

Ingat kembali:

straight a with rightwards arrow on top equals open parentheses table row cell straight x subscript 1 end cell row cell straight y subscript 1 end cell end table close parentheses rightwards arrow open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of straight x subscript 1 squared plus straight y subscript 1 squared end root 

Diketahui straight v with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 4 end table close parentheses, maka:

open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of open parentheses negative 2 close parentheses squared plus 4 squared end root open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of 4 plus 16 end root open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of 20 open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of 4 cross times 5 end root open vertical bar straight v with rightwards arrow on top close vertical bar equals 2 square root of 5 

Jadi, jawaban yang benar adalah C.

0

Roboguru

Panjang vektor adalah

Pembahasan Soal:

Rumus panjang vektor begin mathsize 14px style straight a with rightwards arrow on top equals open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of straight x squared plus straight y squared end root end style dengan vektor begin mathsize 14px style straight a with rightwards arrow on top equals open parentheses table row straight x row straight y 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 straight v with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell 2 square root of 13 end cell end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Diketahui vektor dan . Hitunglah , , dan !

Pembahasan Soal:

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 

 

0

Roboguru

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