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Diketahui vektor . Carilah nilai dari a. Carilah nilai dari

Pertanyaan

Diketahui vektor begin mathsize 14px style k with rightwards arrow on top equals open parentheses table row 7 row 2 end table close parentheses comma space l with rightwards arrow on top equals open parentheses table row 6 row cell negative 1 end cell end table close parentheses comma space dan space m with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 2 end table close parentheses end style. Carilah nilai dari

a. Carilah nilai dari begin mathsize 14px style open vertical bar k with rightwards arrow on top plus l with rightwards arrow on top close vertical bar end style 

Pembahasan Video:

Pembahasan Soal:

Diketahui vektor begin mathsize 14px style k with rightwards arrow on top equals open parentheses table row 7 row 2 end table close parentheses comma space l with rightwards arrow on top equals open parentheses table row 6 row cell negative 1 end cell end table close parentheses end style, dan begin mathsize 14px style m with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 2 end table close parentheses space end style, maka:

begin mathsize 14px style k with rightwards arrow on top plus l with rightwards arrow on top equals open parentheses table row 7 row 2 end table close parentheses plus open parentheses table row 6 row cell negative 1 end cell end table close parentheses equals open parentheses table row cell 7 plus 6 end cell row cell 2 plus left parenthesis negative 1 right parenthesis end cell end table close parentheses equals open parentheses table row 13 row 1 end table close parentheses end style 

Akibatnya:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line k with rightwards arrow on top plus l with rightwards arrow on top vertical line end cell equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of 13 squared plus 1 squared end root end cell row blank equals cell square root of 169 plus 1 end root end cell row blank equals cell square root of 170 end cell end table end style   

Jadi, jawaban yang benar adalah begin mathsize 14px style square root of 170 end style.

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Dijawab oleh:

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Terakhir diupdate 03 Mei 2021

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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

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:

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:

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

Dari soal nomor 9 tunjukkan bahwa . Soal nomor 9. Vektor kolom  dan  didefinisikan sebagai  dan  diberikan  tentukan nilai  dan !

Pembahasan Soal:

Berdasarkan jawaban soal sebelumnya diperoleh nilai a equals 3 dan b equals 13 over 2.

Sehingga diperoleh

vektor p with rightwards arrow on top equals open parentheses table row cell 11 minus a end cell row cell 5 minus b end cell end table close parentheses equals open parentheses table row cell 11 minus 3 end cell row cell 5 minus 13 over 2 end cell end table close parentheses equals open parentheses table row 8 row cell negative 3 over 2 end cell end table close parentheses

vektor q with rightwards arrow on top equals open parentheses table row cell a plus 5 end cell row cell b minus 8 end cell end table close parentheses equals open parentheses table row cell 3 plus 5 end cell row cell 13 over 2 minus 8 end cell end table close parentheses equals open parentheses table row 8 row cell negative 3 over 2 end cell end table close parentheses

Akan ditunjukkan bahwa open vertical bar p with rightwards arrow on top close vertical bar equals open vertical bar q with rightwards arrow on top close vertical bar equals square root of 265 over 4 end root.

open vertical bar p with rightwards arrow on top close vertical bar equals square root of 8 squared plus open parentheses negative 3 over 2 close parentheses squared end root equals square root of 64 plus 9 over 4 end root equals square root of fraction numerator 256 plus 9 over denominator 4 end fraction end root equals square root of 265 over 4 end root 

Karena p with rightwards arrow on top equals q with rightwards arrow on top, maka terbukti bahwa open vertical bar p with rightwards arrow on top close vertical bar equals open vertical bar q with rightwards arrow on top close vertical bar equals square root of 265 over 4 end root.

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