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Jika  dan , nilai dari  adalah ....

Pertanyaan

Jika P open parentheses 4 comma 6 close parentheses dan Q open parentheses 7 comma 8 close parentheses, nilai dari open vertical bar top enclose PQ close vertical bar adalah .... 

  1. square root of 5

  2. square root of 10

  3. square root of 11

  4. square root of 13 

  5. square root of 15

Pembahasan Soal:

Jika P open parentheses 4 comma 6 close parentheses dan Q open parentheses 7 comma 8 close parentheses, nilai dari open vertical bar top enclose PQ close vertical bar adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar top enclose PQ close vertical bar end cell equals cell open vertical bar Q bond P close vertical bar end cell row blank equals cell open vertical bar open parentheses 7 comma 8 close parentheses minus sign open parentheses 4 comma 6 close parentheses close vertical bar end cell row blank equals cell open vertical bar open parentheses 7 minus sign 4 comma 8 minus sign 6 close parentheses close vertical bar end cell row blank equals cell open vertical bar open parentheses 3 comma 2 close parentheses close vertical bar end cell row blank equals cell square root of 3 squared plus 2 squared end root end cell row blank equals cell square root of 9 plus 4 end root end cell row blank equals cell square root of 13 end cell end table

Jadi, jawaban yang tepat adalah D.
 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Umi

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 01 Mei 2021

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Pertanyaan yang serupa

Tentukan panjang vektor dari , jika  dan

Pembahasan Soal:

Diketahui:

a with rightwards arrow on top equals open parentheses 2 comma negative 1 close parentheses

b with rightwards arrow on top equals open parentheses 1 comma negative 2 close parentheses

Ditanya:

panjang vektor dari a with rightwards arrow on top plus b with rightwards arrow on top=?

Jawab:

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 1 row cell negative 2 end cell end table close parentheses equals open parentheses table row 3 row cell negative 3 end cell end table close parentheses open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals square root of 3 squared plus open parentheses negative 3 close parentheses squared end root equals square root of 9 plus 9 end root equals square root of 18 equals 3 square root of 2 .

Jadi, panjang vektor dari a with rightwards arrow on top plus b with rightwards arrow on top adalah 3 square root of 2.

Jadi, jawaban yang tepat adalah B.

Roboguru

Diketahui vektor-vektor , , dan . Tentukan: a.  b.

Pembahasan Soal:

Gunakan konsep penjumlahan vektor dan panjang vektor.

m with rightwards arrow on top equals m subscript 1 i with rightwards arrow on top plus m subscript 2 j with rightwards arrow on top rightwards arrow open vertical bar m with rightwards arrow on top close vertical bar equals square root of open parentheses m subscript 1 close parentheses squared plus open parentheses m subscript 2 close parentheses squared end root

Diketahui vektor-vektor a with rightwards arrow on top equals i with rightwards arrow on top plus 2 j with rightwards arrow on topb with rightwards arrow on top equals 3 i with rightwards arrow on top plus j with rightwards arrow on top, dan c with rightwards arrow on top equals i with rightwards arrow on top plus 9 j with rightwards arrow on top.

a. Akan ditentukan vektor a with rightwards arrow on top plus b with rightwards arrow on top.

Penjumlahan vektor secara aljabar dengan menjumlahkan unsur-unsur yang seletak.

table attributes columnalign right center left columnspacing 2px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell open parentheses i with rightwards arrow on top plus 2 j with rightwards arrow on top close parentheses plus open parentheses 3 i with rightwards arrow on top plus j with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 1 plus 3 close parentheses i with rightwards arrow on top plus open parentheses 2 plus 1 close parentheses j with rightwards arrow on top end cell row blank equals cell 4 i with rightwards arrow on top plus 3 j with rightwards arrow on top end cell end table

b. Akan ditentukan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px 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 open parentheses 4 close parentheses squared plus open parentheses 3 close parentheses squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table

Jadi, diperoleh a with rightwards arrow on top plus b with rightwards arrow on top equals 4 i with rightwards arrow on top plus 3 j with rightwards arrow on top dan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals 5.

Roboguru

Diketahui , dan . Panjang vektor

Pembahasan Soal:

Pertama, substitusikan begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of 2 comma space open vertical bar b with rightwards arrow on top close vertical bar equals 2 end style pada hasil kuadrat dari begin mathsize 14px style vertical line a with rightwards arrow on top minus b with rightwards arrow on top vertical line end style size 14px equals size 14px 3.

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 minus b with rightwards arrow on top close vertical bar squared end cell equals cell 3 squared end cell row cell open vertical bar a with rightwards arrow on top close vertical bar squared minus 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus open vertical bar b with rightwards arrow on top close vertical bar squared end cell equals 9 row cell open parentheses square root of 2 close parentheses squared minus 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus 2 squared end cell equals 9 row cell 2 minus 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus 4 end cell equals 9 row cell negative 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar end cell equals cell 9 minus 2 minus 4 end cell row cell negative 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar end cell equals 3 row cell open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar end cell equals cell negative 3 over 2 end cell end table end style 

Sehingga,

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 squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus open vertical bar b with rightwards arrow on top close vertical bar squared end cell row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar squared end cell equals cell open parentheses square root of 2 close parentheses squared plus 2 open parentheses negative 3 over 2 close parentheses plus 2 squared end cell row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar squared end cell equals cell 2 minus 3 plus 4 end cell row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar squared end cell equals 3 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 plus-or-minus square root of 3 end cell end table end style 

Jadi, jawaban yang tepat adalah A.

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.

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.

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