Roboguru

Diketahui  dan . Jika  maka vektor a dapat dinyatakan ....

Pertanyaan

Diketahui a with rightwards arrow on top equals t i with rightwards arrow on top minus 8 j with rightwards arrow on top plus h k with rightwards arrow on top dan b with rightwards arrow on top equals open parentheses t plus 2 close parentheses i with rightwards arrow on top plus 4 j with rightwards arrow on top plus 2 k with rightwards arrow on top. Jika begin mathsize 14px style a with rightwards arrow on top equals negative b with rightwards arrow on top end style maka vektor a dapat dinyatakan .... 

Pembahasan Soal:

Diketahui:

a with rightwards arrow on top equals t i with rightwards arrow on top minus 8 j with rightwards arrow on top plus h k with rightwards arrow on top

b with rightwards arrow on top equals open parentheses t plus 2 close parentheses i with rightwards arrow on top plus 4 j with rightwards arrow on top plus 2 k with rightwards arrow on top

begin mathsize 14px style a with rightwards arrow on top equals negative b with rightwards arrow on top end style

Ditanya:

Vektor a = ?

Jawab:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell negative b with rightwards arrow on top end cell row cell open square brackets table row t row cell negative 8 end cell row h end table close square brackets end cell equals cell negative open square brackets table row cell t plus 2 end cell row 4 row 2 end table close square brackets end cell row blank left right arrow cell t equals negative left parenthesis t plus 2 right parenthesis end cell row cell negative 8 end cell not equal to cell negative 4 end cell row straight h equals cell negative 2 end cell row blank blank blank row blank blank cell soal space di space atas space tidak space dapat space dikerjakan end cell end table 

Jika kita asumsikan a with rightwards arrow on top equals negative 2 b with rightwards arrow on top, maka soal di atas dapat diselesaikan

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell negative 2 b with rightwards arrow on top end cell row cell open square brackets table row t row cell negative 8 end cell row h end table close square brackets end cell equals cell negative 2 open square brackets table row cell t plus 2 end cell row 4 row 2 end table close square brackets end cell row blank left right arrow cell t equals negative 2 open parentheses t plus 2 close parentheses end cell row t equals cell negative 2 t minus 4 end cell row cell 3 t end cell equals cell negative 4 end cell row t equals cell negative 4 over 3 end cell row cell negative 8 end cell equals cell negative 2 open parentheses 4 close parentheses end cell row cell negative 8 end cell equals cell negative 8 end cell row h equals cell negative 2 times 2 end cell row h equals cell negative 4 end cell row blank blank blank end table 

Jadi, vektor a dapat dinyatakan menjadi a with rightwards arrow on top equals negative 4 over 3 i with rightwards arrow on top minus 8 j with rightwards arrow on top minus 4 k with rightwards arrow on top.

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Mustikowati

Mahasiswa/Alumni Universitas Negeri Jakarta

Terakhir diupdate 03 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui vektor  dan . Jika vektor  memenuhi persamaan  hasil operasi  adalah ...

Pembahasan Soal:

Tentukan vektor begin mathsize 14px style r with rightwards arrow on top end style dari persamaan begin mathsize 14px style 2 r with rightwards arrow on top plus 5 p with rightwards arrow on top equals 3 q with rightwards arrow on top plus 4 r with rightwards arrow on top end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 r with rightwards arrow on top plus 5 p with rightwards arrow on top end cell equals cell 3 q with rightwards arrow on top plus 4 r with rightwards arrow on top end cell row cell 2 r with rightwards arrow on top minus 4 r with rightwards arrow on top end cell equals cell 3 q with rightwards arrow on top minus 5 p with rightwards arrow on top end cell row cell negative 2 r with rightwards arrow on top end cell equals cell 3 q with rightwards arrow on top minus 5 p with rightwards arrow on top end cell row cell negative 2 r with rightwards arrow on top end cell equals cell 3 open parentheses table row 2 row 5 row cell negative 3 end cell end table close parentheses minus 5 open parentheses table row 3 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell row cell negative 2 r with rightwards arrow on top end cell equals cell open parentheses table row cell 3 times 2 minus 5 times 3 end cell row cell 3 times 5 minus 5 times left parenthesis negative 2 right parenthesis end cell row cell 3 times left parenthesis negative 3 right parenthesis minus 5 times left parenthesis negative 1 right parenthesis end cell end table close parentheses end cell row cell negative 2 r with rightwards arrow on top end cell equals cell open parentheses table row cell 6 minus 15 end cell row cell 15 plus 10 end cell row cell negative 9 plus 5 end cell end table close parentheses end cell row cell negative 2 r with rightwards arrow on top end cell equals cell open parentheses table row cell negative 9 end cell row 25 row cell negative 4 end cell end table close parentheses end cell row cell r with rightwards arrow on top end cell equals cell negative 1 half open parentheses table row cell negative 9 end cell row 25 row cell negative 4 end cell end table close parentheses end cell row cell r with rightwards arrow on top end cell equals cell open parentheses table row cell 9 over 2 end cell row cell negative 25 over 2 end cell row 2 end table close parentheses end cell end table end style 

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top plus q with rightwards arrow on top plus 2 r with rightwards arrow on top end cell equals cell open parentheses table row 3 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses plus open parentheses table row 2 row 5 row cell negative 3 end cell end table close parentheses plus 2 open parentheses table row cell 9 over 2 end cell row cell negative 25 over 2 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus 2 plus 2 times 9 over 2 end cell row cell negative 2 plus 5 plus 2 times open parentheses negative 25 over 2 close parentheses end cell row cell negative 1 plus left parenthesis negative 3 right parenthesis plus 2 times 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus 2 plus 9 end cell row cell negative 2 plus 5 minus 25 end cell row cell negative 1 minus 3 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 14 row cell negative 22 end cell row 0 end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah C.

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Roboguru

Diketahui koordinat titik . Jika KL= MN koordinat titik N adalah ...

Pembahasan Soal:

Misal koordinat titik begin mathsize 14px style N left parenthesis straight a comma straight b comma straight c right parenthesis end style maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell K L end cell equals cell M N end cell row cell L minus K end cell equals cell N minus M end cell row cell open parentheses table row 2 row 8 row cell negative 2 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row 5 row cell negative 4 end cell end table close parentheses end cell equals cell table row cell open parentheses table row a row b row c end table close parentheses end cell end table minus table row cell table row cell table row cell open parentheses table row 5 row 3 row cell negative 3 end cell end table close parentheses end cell end table end cell end table end cell end table end cell row cell open parentheses table row cell table row 3 row 3 row 2 end table end cell end table close parentheses end cell equals cell open parentheses table row cell table row cell a minus 5 end cell row cell b minus 3 end cell row cell c plus 3 end cell end table end cell end table close parentheses end cell row cell open parentheses table row cell 3 plus 5 end cell row cell 3 plus 3 end cell row cell 2 minus 3 end cell end table close parentheses end cell equals cell open parentheses table row a row b row c end table close parentheses end cell row cell open parentheses table row 8 row 6 row cell negative 1 end cell end table close parentheses end cell equals cell open parentheses table row a row b row c end table close parentheses end cell end table end style

jadi koordinat titik begin mathsize 14px style N open parentheses 8 comma 6 comma negative 1 close parentheses end style 

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Diketahui  dan . Vektor yang tegak lurus terhadap kedua vektor tersebut adalah ....

Pembahasan Soal:

Diketahui: a with rightwards harpoon with barb upwards on top equals 3 i minus j plus 2 k dan b with rightwards harpoon with barb upwards on top equals i plus 2 j minus 2 k

Sehingga, 

  • a with rightwards harpoon with barb upwards on top subscript x equals 3 comma space a with rightwards harpoon with barb upwards on top subscript y equals negative 1 comma space a with rightwards harpoon with barb upwards on top subscript z equals 2 
  • b with rightwards harpoon with barb upwards on top subscript x equals 1 comma space b with rightwards harpoon with barb upwards on top subscript y equals 2 comma space b with rightwards harpoon with barb upwards on top subscript z equals negative 2 

Vektor yang tegak lurus dengan vektor a with rightwards harpoon with barb upwards on top dan vektor b with rightwards harpoon with barb upwards on top merupakan vektor hasil dari perkalian silang a with rightwards harpoon with barb upwards on top cross times b with rightwards harpoon with barb upwards on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top cross times b with rightwards harpoon with barb upwards on top end cell equals cell open parentheses a with rightwards harpoon with barb upwards on top subscript y b with rightwards harpoon with barb upwards on top subscript z minus a with rightwards harpoon with barb upwards on top subscript z b with rightwards harpoon with barb upwards on top subscript y close parentheses i plus open parentheses a with rightwards harpoon with barb upwards on top subscript z b with rightwards harpoon with barb upwards on top subscript x minus a with rightwards harpoon with barb upwards on top subscript x b with rightwards harpoon with barb upwards on top subscript z close parentheses j end cell row blank blank cell plus open parentheses a with rightwards harpoon with barb upwards on top subscript x b with rightwards harpoon with barb upwards on top subscript y minus a with rightwards harpoon with barb upwards on top subscript y b with rightwards harpoon with barb upwards on top subscript x close parentheses k end cell row blank equals cell open parentheses open parentheses negative 1 close parentheses times open parentheses negative 2 close parentheses minus 2 times 2 close parentheses i plus open parentheses 2 times 1 minus 3 times open parentheses negative 2 close parentheses close parentheses j end cell row blank blank cell plus open parentheses 3 times 2 minus open parentheses negative 1 close parentheses times 1 close parentheses k end cell row blank equals cell open parentheses 2 minus 4 close parentheses i plus open parentheses 2 plus 6 close parentheses j plus open parentheses 6 plus 1 close parentheses k end cell row blank equals cell negative 2 i minus 8 j plus 7 k end cell end table     

Jadi, vektor yang tegak lurus terhadap kedua vektor tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 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 cross times 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 minus 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 i 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 8 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 plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table.

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Roboguru

Diketahui titik A(-2,1,5) terletak pada garis dengan vektor penunjuk arahnya yaitu . Persamaan vektor dari garis tersebut adalah ....

Pembahasan Soal:

Karena koordinat titik A adalah (-2,1,5), maka vektor posisi titik A terhadap titik (0,0,0) adalah begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 1 row 5 end table close parentheses end style.

Diketahui pula bahwa vektor penunjuk arahnya yaitu undefined.

Maka persamaan vektor dari garis tersebut adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus t p with rightwards arrow on top end cell row cell r with rightwards arrow on top end cell equals cell open parentheses table row cell negative 2 end cell row 1 row 5 end table close parentheses plus t open parentheses table row 4 row cell negative 2 end cell row 1 end table close parentheses end cell end table end style  

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Roboguru

Diketahui  dan C titik pada AB sedemikian sehingga  Tentukan vektor  dalam bentuk  kemudian tentukan koordinat titik C.

Pembahasan Soal:

Diketahui A left parenthesis 2 comma 7 comma 8 right parenthesis comma space B left parenthesis negative 1 comma 1 comma negative 1 right parenthesis maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell B with rightwards arrow on top minus A with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 1 end cell row 1 row cell negative 1 end cell end table close parentheses minus open parentheses table row 2 row 7 row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row cell negative 6 end cell row cell negative 9 end cell end table close parentheses end cell end table 

Selanjutnya, 

table attributes columnalign right center left columnspacing 0px end attributes row C equals cell 1 third A B end cell row blank equals cell 1 third open parentheses table row cell negative 3 end cell 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 1 end cell row cell negative 2 end cell row cell negative 3 end cell end table close parentheses end cell end table 

Diperoleh nilai AC:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A C with rightwards arrow on top end cell equals cell C with rightwards arrow on top minus A with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 1 end cell row cell negative 2 end cell row cell negative 3 end cell end table close parentheses minus open parentheses table row 2 row 7 row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row cell negative 9 end cell row cell negative 11 end cell end table close parentheses end cell end table 

Dengan demikian, vektor AC adalah stack A C with rightwards arrow on top equals negative 3 i with rightwards arrow on top minus 9 j with rightwards arrow on top minus 11 k with rightwards arrow on top dan koordinat titik C adalah C left parenthesis negative 1 comma negative 2 comma negative 3 right parenthesis. 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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