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Panjang dari vektor  adalah ...

Pertanyaan

Panjang dari vektor a with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 6 end table close parentheses adalah ...

Pembahasan Soal:

Panjang vektor u with rightwards arrow on top equals open parentheses table row a row b end table close parentheses adalah open vertical bar u with rightwards arrow on top close vertical bar equals square root of a squared plus b squared end root.

Maka 

Panjang dari vektor a with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 6 end table close parentheses adalah

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 open parentheses negative 1 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 1 plus 36 end root end cell row blank equals cell square root of 37 end cell end table 

Dengan demikian, panjang dari vektor a with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 6 end table close parentheses adalah open vertical bar a with rightwards arrow on top close vertical bar equals square root of 37

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Rante

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 04 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

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.

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 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.

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.

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.

Roboguru

Diketahui . Tentukanlah: a.

Pembahasan Soal:

begin mathsize 14px style a with rightwards arrow on top plus 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 a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell open parentheses table row 3 row cell negative 1 end cell end table close parentheses plus open parentheses table row 2 row 13 end table close parentheses end cell row blank equals cell open parentheses table row 5 row 12 end table close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell end table end style didapatkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals cell square root of 5 squared plus 12 squared end root end cell row blank equals cell square root of 25 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 end table end style

Dengan demikian, begin mathsize 14px style a with rightwards arrow on top plus b with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row 5 row 12 end table close parentheses end style dan begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell end table end style adalah begin mathsize 14px style 13 end style.

Roboguru

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