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Diketahui vektor . Carilah nilai dari b. Tentukan nilai

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 d a n 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

b. Tentukan nilai begin mathsize 14px style open parentheses m with rightwards arrow on top times open parentheses k with rightwards arrow on top plus l with rightwards arrow on top close parentheses close parentheses end style 

Pembahasan Video:

Pembahasan Soal:

Ingat!

begin mathsize 14px style a with rightwards arrow on top times b 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 times open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses equals open parentheses a subscript 1 times b subscript 1 close parentheses plus open parentheses a subscript 2 times b subscript 2 close parentheses end style 

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 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell k with rightwards arrow on top plus l with rightwards arrow on top end cell equals cell 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 end cell row blank equals cell open parentheses table row cell 7 plus 6 end cell row cell 2 plus open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 13 row 1 end table close parentheses end cell end table end style  

Akibatnya:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses m with rightwards arrow on top times open parentheses k with rightwards arrow on top plus l with rightwards arrow on top close parentheses close parentheses end cell equals cell open parentheses table row cell negative 2 end cell row 2 end table close parentheses times open parentheses table row 13 row 1 end table close parentheses end cell row blank equals cell open parentheses negative 2 close parentheses times 13 plus 2 times 1 end cell row blank equals cell negative 26 plus 2 end cell row blank equals cell negative 24 end cell end table end style   

Jadi, jawaban yang benar adalah begin mathsize 14px style negative 24 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Freelancer7

Terakhir diupdate 03 Mei 2021

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Pertanyaan yang serupa

Diketahui vektor-vektor sebagai berikut: Gambarlah vektor: a.

Pembahasan Soal:

Pada soal diketahu vektor begin mathsize 14px style a with rightwards arrow on top end style, buatlah sebuah garis lurus sesuai dengan arah vektor pada soal sepanjang begin mathsize 14px style 3 over 5 end style dari vektor begin mathsize 14px style a with rightwards arrow on top end style dan berilah tanda panah di ujung garis tersebut (titik akhir garis), sehingga diperoleh gambar berikut: 

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

Vektor-vektor posisi dari A, B, dan C adalah . Hitunglah setiap vektor berikut. e.

Pembahasan Soal:

Kita dapat langsung menghitung dari setiap operasi vektor tersebut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 3 c with rightwards arrow on top end cell equals cell 2 open parentheses table row 4 row 3 end table close parentheses plus open parentheses table row cell negative 2 end cell row 3 end table close parentheses minus 3 open parentheses table row 1 row 5 end table close parentheses end cell row blank equals cell open parentheses table row 8 row 6 end table close parentheses plus open parentheses table row cell negative 2 end cell row 3 end table close parentheses minus open parentheses table row 3 row 15 end table close parentheses end cell row blank equals cell open parentheses table row cell 8 minus 2 minus 3 end cell row cell 6 plus 3 minus 15 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 6 end cell end table close parentheses end cell end table end style

Jadi, hasil dari begin mathsize 14px style 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 a with rightwards arrow on top end cell 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 cell b 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell c with rightwards arrow on top end cell end table end style adalah begin mathsize 14px style open parentheses table row 3 row cell negative 6 end cell end table close parentheses end style

0

Roboguru

Diketahui vektor  dan . Tentukan .

Pembahasan Soal:

Inget kembali perkalian vektor dengan skalar berikut ini.

k times open parentheses table row cell a subscript 1 end cell row cell a subscript 3 end cell row cell a subscript 3 end cell end table close parentheses equals open parentheses table row cell k a subscript 1 end cell row cell k a subscript 2 end cell row cell k a subscript 3 end cell end table close parentheses

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row cell a subscript 1 plus b subscript 1 end cell row cell a subscript 2 plus b subscript 2 end cell row cell a subscript 3 plus b subscript 3 end cell end table close parentheses 

Oleh karena itu, kita peroleh hasil berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 half u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell negative 1 half open parentheses table row cell negative 4 end cell row 8 row 2 end table close parentheses plus 2 open parentheses table row 5 row 1 row cell negative 4 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 1 end cell end table close parentheses plus open parentheses table row 10 row 2 row cell negative 8 end cell end table close parentheses end cell row blank blank blank row blank equals cell open parentheses table row 12 row cell negative 2 end cell row cell negative 9 end cell end table close parentheses end cell end table   

Jadi,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 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top end cell 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell v 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 table row cell open parentheses table row 12 row cell negative 2 end cell row cell negative 9 end cell end table close parentheses end cell end table end cell end table 

0

Roboguru

Pembahasan Soal:

a with rightwards harpoon with barb upwards on top equals 3 i with rightwards harpoon with barb upwards on top minus 2 j with rightwards harpoon with barb upwards on top plus k with rightwards harpoon with barb upwards on top equals open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses  b with rightwards harpoon with barb upwards on top equals 2 i with rightwards harpoon with barb upwards on top minus 3 k with rightwards harpoon with barb upwards on top equals open parentheses table row 2 row 0 row cell negative 3 end cell end table close parentheses  c with rightwards harpoon with barb upwards on top equals j with rightwards harpoon with barb upwards on top minus 2 k with rightwards harpoon with barb upwards on top equals open parentheses table row 0 row 1 row cell negative 2 end cell end table close parentheses  2 a with rightwards harpoon with barb upwards on top minus 3 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top  2 open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses minus 3 open parentheses table row 2 row 0 row cell negative 3 end cell end table close parentheses plus open parentheses table row 0 row 1 row cell negative 2 end cell end table close parentheses equals open parentheses table row 6 row cell negative 4 end cell row 2 end table close parentheses minus open parentheses table row 6 row 0 row cell negative 9 end cell end table close parentheses plus open parentheses table row 0 row 1 row cell negative 2 end cell end table close parentheses equals open parentheses table row 0 row cell negative 3 end cell row 9 end table close parentheses equals negative 3 j with rightwards harpoon with barb upwards on top plus 9 k with rightwards harpoon with barb upwards on top

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Roboguru

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