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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 stack 3 a with rightwards harpoon with barb upwards on top times stack 2 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 stack 3 a with rightwards harpoon with barb upwards on top times 2 b with rightwards harpoon with barb upwards on top end cell equals cell 3 open square brackets table row 1 row 3 row cell negative 2 end cell end table close square brackets times 2 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 3 row 9 row cell negative 6 end cell end table close square brackets times open square brackets table row 8 row cell negative 4 end cell row 8 end table close square brackets end cell row blank equals cell open square brackets table row cell 24 plus open parentheses negative 12 close parentheses plus 24 end cell row cell 72 plus open parentheses negative 36 close parentheses plus 72 end cell row cell negative 48 plus 24 plus open parentheses negative 48 close parentheses end cell end table close square brackets end cell row blank equals cell open square brackets table row 36 row 108 row cell negative 72 end cell end table close square brackets end cell row blank equals cell 36 i plus 108 j minus 72 k end cell end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack 3 a with rightwards harpoon with barb upwards on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards harpoon with barb upwards 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 36 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 108 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 72 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table.

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.

0

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.

0

Roboguru

Diketahui , , tentukan: a.

Pembahasan Soal:

Hasil dari perkalian vektor dengan skalar tersebut dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top end cell equals cell 3 open parentheses table row cell negative 2 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row 6 end table close parentheses end cell end table end style

Dengan demikian, begin mathsize 14px style 3 a with rightwards arrow on top equals open parentheses table row cell negative 6 end cell row 6 end table close parentheses end style

0

Roboguru

Diketahui vektor , maka vektor adalah...

Pembahasan Soal:

Diketahui vektor begin mathsize 14px style u with rightwards arrow on top equals open square brackets table row 2 row cell negative 3 end cell end table close square brackets space dan space v with rightwards arrow on top equals open square brackets table row cell negative 1 end cell row 5 end table close square brackets end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 u with rightwards arrow on top minus v with rightwards arrow on top end cell equals cell 2 open square brackets table row 2 row cell negative 3 end cell end table close square brackets minus open square brackets table row cell negative 1 end cell row 5 end table close square brackets end cell row blank equals cell open square brackets table row 4 row cell negative 6 end cell end table close square brackets minus open square brackets table row cell negative 1 end cell row 5 end table close square brackets end cell row blank equals cell open square brackets table row 5 row cell negative 11 end cell end table close square brackets end cell end table end style

Jadi diperoleh hasil dari vektor begin mathsize 14px style 2 u with rightwards arrow on top minus v with rightwards arrow on top equals open square brackets table row 5 row cell negative 11 end cell end table close square brackets end style

0

Roboguru

Diketahui vektor  dan . Panjang vektor  adalah ...

Pembahasan Soal:

Jika terdapat vektor a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan skalar k, maka perkalian vektor dengan skalar adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell k a with rightwards arrow on top end cell equals cell k open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell k a subscript 1 end cell row cell k a subscript 2 end cell end table close parentheses end cell end table 

Dan panjang vektor a with rightwards arrow on top adalah:

open vertical bar a with rightwards arrow on top close vertical bar equals square root of a subscript 1 squared plus a subscript 2 squared end root 

Diketahui p with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row cell negative 5 end cell end table close parentheses dan q with rightwards arrow on top equals open parentheses table row cell negative 6 end cell row cell negative 9 end cell end table close parentheses, maka tentukan hasil dari 2 p with rightwards arrow on top minus q with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p with rightwards arrow on top minus q with rightwards arrow on top end cell equals cell 2 open parentheses table row cell negative 2 end cell row cell negative 5 end cell end table close parentheses minus open parentheses table row cell negative 6 end cell row cell negative 9 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 open parentheses negative 2 close parentheses end cell row cell 2 open parentheses negative 5 close parentheses end cell end table close parentheses minus open parentheses table row cell negative 6 end cell row cell negative 9 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 minus open parentheses negative 6 close parentheses end cell row cell negative 10 minus open parentheses negative 9 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 1 end cell end table close parentheses end cell end table 

Sehingga, table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell p with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell q 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 2 row cell negative 1 end cell end table close parentheses end cell end table.

Panjang vektor 2 p with rightwards arrow on top minus q with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 p with rightwards arrow on top minus q close vertical bar end cell equals cell square root of 2 squared plus open parentheses negative 1 close parentheses squared end root end cell row blank equals cell square root of 4 plus 1 end root end cell row blank equals cell square root of 5 end cell end table  

Jadi, jawaban yang tepat adalah C.

0

Roboguru

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