Roboguru

Jika , maka hitunglah !

Pertanyaan

Jika a with rightwards harpoon with barb upwards on top equals i plus 3 j minus 2 k comma space b with rightwards harpoon with barb upwards on top equals 4 i minus 2 j plus 4 k, maka hitunglah a with rightwards harpoon with barb upwards on top times b with rightwards harpoon with barb upwards on top !

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top end cell equals cell i plus 3 j minus 2 k comma space b with rightwards harpoon with barb upwards on top equals 4 i minus 2 j plus 4 k end cell row cell a with rightwards harpoon with barb upwards on top times b with rightwards harpoon with barb upwards on top end cell equals cell open square brackets table row 1 row 3 row cell negative 2 end cell end table close square brackets times open square brackets table row 4 row cell negative 2 end cell row 4 end table close square brackets end cell row blank equals cell open square brackets table row cell 4 plus open parentheses negative 2 close parentheses plus 4 end cell row cell 12 plus open parentheses negative 6 close parentheses plus 12 end cell row cell negative 8 plus 4 plus open parentheses negative 8 close parentheses end cell end table close square brackets end cell row blank equals cell open square brackets table row 6 row 18 row cell negative 12 end cell end table close square brackets end cell row blank equals cell 6 i plus 18 j minus 12 k end cell end table

Jadi, a with rightwards harpoon with barb upwards on top times b with rightwards harpoon with barb upwards on top equals 6 i plus 18 j minus 12 k.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika  dan , tentukan vektor-vektor berikut dan hitung juga besarnya. a.

Pembahasan Soal:

Jika sebuah vektor dikalikan dengan skalar, maka masing-masing elemen vektor tersebut dikalikan dengan skalar. Sehingga, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 bold italic p end cell equals cell 4 times open parentheses table row cell negative 5 end cell row 12 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 times left parenthesis negative 5 right parenthesis end cell row cell 4 times 12 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 20 end cell row 48 end table close parentheses end cell end table end style 

Jadi, hasil dari Error converting from MathML to accessible text.adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 20 end cell row 48 end table close parentheses end cell end table end style.

Roboguru

Jika vektor  dan , vektor  yang memenuhi operasi  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 v with rightwards arrow on top plus 2 w with rightwards arrow on top end cell equals cell u with rightwards arrow on top minus v with rightwards arrow on top end cell row cell 2 w with rightwards arrow on top end cell equals cell u with rightwards arrow on top minus 4 v with rightwards arrow on top end cell row cell 2 w with rightwards arrow on top end cell equals cell open parentheses table row 4 row 6 end table close parentheses minus 4 open parentheses table row 3 row cell negative 1 end cell end table close parentheses end cell row cell 2 w with rightwards arrow on top end cell equals cell open parentheses table row cell 4 minus 4 times 3 end cell row cell 6 minus 4 times open parentheses negative 1 close parentheses end cell end table close parentheses end cell row cell 2 w with rightwards arrow on top end cell equals cell open parentheses table row cell negative 8 end cell row 10 end table close parentheses end cell row cell w with rightwards arrow on top end cell equals cell 1 half open parentheses table row cell negative 8 end cell row 10 end table close parentheses end cell row cell w with rightwards arrow on top end cell equals cell open parentheses table row cell negative 4 end cell row 5 end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah C.

Roboguru

Diketahui titik , dan .

Pembahasan Soal:

MIsalkan terdapat dua buah titik straight A open parentheses straight x subscript 1 comma space straight y subscript 1 comma space straight z subscript 1 close parentheses dan straight B open parentheses straight x subscript 2 comma space straight y subscript 2 comma space straight z subscript 2 close parentheses. Vektor AB dapat didefinisikan sebagai:

AB with rightwards arrow on top equals straight B minus straight A equals open parentheses table row cell straight x subscript 2 minus straight x subscript 1 end cell row cell straight y subscript 2 minus straight y subscript 1 end cell row cell straight z subscript 2 minus straight z subscript 1 end cell end table close parentheses

Berdasarkan definisi vektor di atas, jika diketahui  straight A open parentheses 2 comma space minus 4 comma space 10 close parentheses dan straight B left parenthesis 4 comma space minus 8 comma space 8 right parenthesis  maka vektor AB with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell B minus A end cell row blank equals cell open parentheses table row 4 row cell negative 8 end cell row 8 end table close parentheses minus open parentheses table row 2 row cell negative 4 end cell row 10 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 2 end cell row cell negative 8 plus 4 end cell row cell 8 minus 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 4 end cell row cell negative 2 end cell end table close parentheses end cell end table

Selanjutnya, kita harus mencari formula yang sesuai dengan hasil AB with rightwards arrow on top, maka kita harus menghitung BC with rightwards arrow on top sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell BC with rightwards arrow on top end cell equals cell straight C minus straight B end cell row blank equals cell open parentheses table row cell negative 2 end cell row 4 row 14 end table close parentheses minus open parentheses table row 4 row cell negative 8 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 minus 4 end cell row cell 4 plus 8 end cell row cell 14 minus 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row 12 row 6 end table close parentheses end cell end table

Berdasarkan hasil vektor BC with rightwards arrow on top, perhatikan bahwa elemen-elemen BC with rightwards arrow on top memiliki hubungan kelipatan dengan elemen-elemen AB with rightwards arrow on top, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell BC with rightwards arrow on top end cell equals cell open parentheses table row cell negative 6 end cell row 12 row 6 end table close parentheses end cell row cell BC with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 times 2 end cell row cell negative 3 times open parentheses negative 4 close parentheses end cell row cell negative 3 times open parentheses negative 2 close parentheses end cell end table close parentheses end cell row cell BC with rightwards arrow on top end cell equals cell negative 3 open parentheses table row 2 row cell negative 4 end cell row cell negative 2 end cell end table close parentheses end cell row cell BC with rightwards arrow on top end cell equals cell negative 3 AB with rightwards arrow on top end cell row cell AB with rightwards arrow on top end cell equals cell negative 1 third BC with rightwards arrow on top end cell end table 

Dengan demikian, vektor AB with rightwards arrow on top equals negative 1 third table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell BC with rightwards arrow on top end cell end table.

Oleh karena itu, jawaban yang benar adalah D.

Roboguru

Jika , dan , maka vektor adalah ...

Pembahasan Soal:

Misalkan terdapat vektor straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell end table close parentheses, straight b with rightwards arrow on top equals open parentheses table row cell straight b subscript 1 end cell row cell straight b subscript 2 end cell end table close parentheses dan straight k adalah skalar. maka berlaku:

open parentheses straight i close parentheses space straight a with rightwards arrow on top plus-or-minus straight b with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 plus-or-minus straight b subscript 1 end cell row cell straight a subscript 2 plus-or-minus straight b subscript 2 end cell end table close parentheses left parenthesis ii right parenthesis space straight k straight a with rightwards arrow on top equals open parentheses table row cell ka subscript 1 end cell row cell ka subscript 2 end cell end table close parentheses

Berdasarkan sifat-sifat operasi vektor tersebut, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards arrow on top end cell equals cell straight a with rightwards arrow on top plus 3 straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 2 row cell negative 1 end cell end table close parentheses plus 3 open parentheses table row 4 row cell negative 2 end cell end table close parentheses minus 2 open parentheses table row cell negative 1 end cell row 3 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 12 row cell negative 6 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 6 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell 2 plus 12 plus 2 end cell row cell negative 1 minus 6 minus 6 end cell end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 16 row cell negative 13 end cell end table close parentheses end cell end table

Dengan demikian, hasil operasi vektor pada soal adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight d with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 16 row cell negative 13 end cell end table close parentheses end cell end table.

Oleh karena itu, tidak ada jawaban yang benar.

Roboguru

Jika , , dan , maka  adalah ...

Pembahasan Soal:

Hasil dari operasi hitung vektor tersebut dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x with rightwards arrow on top minus 2 z with rightwards arrow on top minus 3 y with rightwards arrow on top end cell equals cell 5 open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses minus 2 open parentheses table row 2 row 6 row cell negative 1 end cell end table close parentheses minus 3 open parentheses table row 1 row 3 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 15 row cell negative 10 end cell row 5 end table close parentheses minus open parentheses table row 4 row 12 row cell negative 2 end cell end table close parentheses minus open parentheses table row 3 row 9 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 15 minus 4 minus 3 end cell row cell negative 10 minus 12 minus 9 end cell row cell 5 minus open parentheses negative 12 close parentheses minus open parentheses negative 3 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 31 end cell row 20 end table close parentheses end cell end table

Dengan demikian, 5 x with rightwards arrow on top minus 2 z with rightwards arrow on top minus 3 y with rightwards arrow on top equals 8 a with rightwards arrow on top minus 31 b with rightwards arrow on top plus 20 c with rightwards arrow on top 

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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