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Jika a=3i+2j​; b=6i−8j​ dan c=5i−7j​, maka 2a−b+3c=...

Pertanyaan

Jika straight a with bar on top equals 3 straight i with bar on top plus 2 straight j with bar on top; straight b with bar on top equals 6 straight i with bar on top minus 8 straight j with bar on top dan straight c with bar on top equals 5 straight i with bar on top minus 7 straight j with bar on top, maka 2 a with bar on top minus sign b with bar on top plus 3 c with bar on top equals...  

  1. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 15 i with bar on top minus sign 9 j with bar on top end cell end table 

  2. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 16 i with bar on top plus 10 j with bar on top end cell end table 

  3. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 27 i with bar on top plus 33 j with bar on top end cell end table 

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 i with bar on top plus 2 j with bar on top end cell end table 

  5. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 15 i with bar on top plus 9 j with bar on top end cell end table 

Pembahasan Soal:

Dengan menggunakan sifat penjumlahan vektor, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with bar on top minus sign b with bar on top plus 3 c with bar on top end cell equals cell 2 open parentheses table row 3 row 2 end table close parentheses minus sign open parentheses table row 6 row cell negative sign 8 end cell end table close parentheses plus 3 open parentheses table row 5 row cell negative sign 7 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row 4 end table close parentheses minus sign open parentheses table row 6 row cell negative sign 8 end cell end table close parentheses plus open parentheses table row 15 row cell negative sign 21 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 minus sign 6 plus 15 end cell row cell 4 minus sign left parenthesis minus sign 8 right parenthesis plus left parenthesis minus sign 21 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row 15 row 9 end table close parentheses end cell row blank equals cell 15 i with bar on top plus 9 j with bar on top end cell end table 

Maka, table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with bar on top minus sign b with bar on top plus 3 c with bar on top end cell equals cell 15 i with bar on top plus 9 j with bar on top end cell end table.

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Nadidah

Mahasiswa/Alumni Universitas Nasional

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Diketahui vektor-vektor a=i+2j​−3k, b=3i+5k, c=−2i−4j​+k. Vektor 2a+b−c=....

Pembahasan Soal:

Secara aljabar hasil penjumlahan antara vektor begin mathsize 14px style a with rightwards arrow on top space dan space b with rightwards arrow on top end style adalah

begin mathsize 14px style a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses a subscript 1 plus b subscript 1 close parentheses i with rightwards arrow on top plus open parentheses a subscript 2 plus b subscript 2 close parentheses j with rightwards arrow on top plus open parentheses a subscript 3 plus b subscript 3 close parentheses k with rightwards arrow on top end style

Sehingga,

begin mathsize 14px style 2 a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top equals 2 open parentheses i with rightwards arrow on top plus 2 j with rightwards arrow on top minus 3 k with rightwards arrow on top close parentheses plus open parentheses 3 i with rightwards arrow on top plus 5 k with rightwards arrow on top close parentheses minus open parentheses negative 2 i with rightwards arrow on top minus 4 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses equals open parentheses 2 i with rightwards arrow on top plus 4 j with rightwards arrow on top minus 6 k with rightwards arrow on top close parentheses plus open parentheses 3 i with rightwards arrow on top plus 5 k with rightwards arrow on top close parentheses minus open parentheses negative 2 i with rightwards arrow on top minus 4 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses equals open parentheses 2 plus 3 minus open parentheses negative 2 close parentheses close parentheses i with rightwards arrow on top plus open parentheses 4 minus open parentheses negative 4 close parentheses close parentheses j with rightwards arrow on top plus open parentheses negative 6 plus 5 minus 1 close parentheses k with rightwards arrow on top equals 7 i with rightwards arrow on top plus 8 j with rightwards arrow on top minus 2 k with rightwards arrow on top end style

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Diketahui a=(−4−5​), b=(62​), dan c=(3−4​). Hitunglah: c.  3a−b−c

Pembahasan Soal:

Dengan menggunakan konsep selisih dua vektor dan perkalian vektor dengan skalar diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a minus b minus c end cell equals cell 3 open parentheses table row cell negative 4 end cell row cell negative 5 end cell end table close parentheses minus open parentheses table row 6 row 2 end table close parentheses minus open parentheses table row 3 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 12 end cell row cell negative 15 end cell end table close parentheses minus open parentheses table row 6 row 2 end table close parentheses minus open parentheses table row 3 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 12 minus 6 minus 3 end cell row cell negative 15 minus 2 minus open parentheses negative 4 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 21 end cell row cell negative 13 end cell end table close parentheses end cell end table end style

Dengan demikian hasil daribegin mathsize 14px style 3 a minus b minus c end style adalah begin mathsize 14px style open parentheses table row cell negative 21 end cell row cell negative 13 end cell end table close parentheses end style.

0

Roboguru

Diketahui vektor-vektor a=i+2j​−3k, b=3i+5k, c=−2i−4j​+k, dan u=2a+b−c. Vektor u = ...

Pembahasan Soal:

begin mathsize 12px style u with rightwards arrow on top equals 2 a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top  u with rightwards arrow on top equals 2 open parentheses i plus 2 j minus 3 k close parentheses plus open parentheses 3 i plus 5 k close parentheses minus open parentheses negative 2 i minus 4 j plus k close parentheses  u with rightwards arrow on top equals open parentheses 2 i plus 4 j minus 6 k close parentheses plus open parentheses 3 i plus 5 k close parentheses plus open parentheses 2 i plus 4 j minus k close parentheses  u with rightwards arrow on top equals 7 i plus 8 j minus 2 k end style

0

Roboguru

Diketahui . Jika 4u−3v=nw, maka  adalah ….

Pembahasan Soal:

Perhatikan bahwa,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 straight u with rightwards arrow on top minus 3 straight v with rightwards arrow on top end cell equals cell straight n straight w with rightwards arrow on top end cell row cell 4 open parentheses table row cell negative 2 end cell row 4 row 8 end table close parentheses minus 3 open parentheses table row 4 row 2 row 6 end table close parentheses end cell equals cell straight n open parentheses table row 10 row cell negative 5 end cell row cell negative 7 end cell end table close parentheses end cell row cell open parentheses table row cell negative 8 end cell row 16 row 32 end table close parentheses minus open parentheses table row 12 row 6 row 18 end table close parentheses end cell equals cell open parentheses table row cell 10 straight n end cell row cell negative 5 straight n end cell row cell negative 7 straight n end cell end table close parentheses end cell row cell open parentheses table row cell negative 8 minus 12 end cell row cell 16 minus 6 end cell row cell 32 minus 18 end cell end table close parentheses end cell equals cell open parentheses table row cell 10 straight n end cell row cell negative 5 straight n end cell row cell negative 7 straight n end cell end table close parentheses end cell row cell open parentheses table row cell negative 20 end cell row 10 row 14 end table close parentheses end cell equals cell open parentheses table row cell 10 straight n end cell row cell negative 5 straight n end cell row cell negative 7 straight n end cell end table close parentheses end cell end table end style 

Perhatikan pada baris pertama

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 20 end cell equals cell 10 straight n end cell row cell negative 2 end cell equals straight n end table end style 

Diperoleh begin mathsize 14px style straight n equals negative 2 end style, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight n open parentheses straight u with rightwards arrow on top minus straight v with rightwards arrow on top close parentheses end cell equals cell negative 2 open parentheses table row cell negative 2 minus 4 end cell row cell 4 minus 2 end cell row cell 8 minus 6 end cell end table close parentheses end cell row blank equals cell negative 2 open parentheses table row cell negative 6 end cell row 2 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 12 row cell negative 4 end cell row cell negative 4 end cell end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah C.space space  

0

Roboguru

Diketahui . Jika a=p​−q​+2r, maka vektor satuan dari a adalah ….

Pembahasan Soal:

Perhatikan bahwa,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top end cell equals cell straight p with rightwards arrow on top minus straight q with rightwards arrow on top plus 2 straight r with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row cell negative 5 end cell row 4 end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 2 end table close parentheses plus 2 open parentheses table row 2 row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 5 end cell row 4 end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 2 end table close parentheses plus open parentheses table row 4 row 4 row cell negative 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 minus 3 plus 4 end cell row cell negative 5 minus open parentheses negative 1 close parentheses plus 4 end cell row cell 4 minus 2 plus open parentheses negative 6 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row 0 row cell negative 4 end cell 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 open vertical bar straight a with rightwards arrow on top close vertical bar end cell equals cell square root of 3 squared plus 0 squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 9 plus 0 plus 16 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table end style 

Diperoleh vektor satuan undefined adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight e subscript straight a with rightwards arrow on top end subscript end cell equals cell fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row 3 row 0 row cell negative 4 end cell end table close parentheses over denominator 5 end fraction end cell row blank equals cell 1 fifth open parentheses table row 3 row 0 row cell negative 4 end cell end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah C.space space  

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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