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Jika diketahui adalah

Pertanyaan

Jika diketahui straight k with rightwards harpoon with barb upwards on top equals open parentheses 7 comma 2 close parentheses comma straight m with rightwards harpoon with barb upwards on top equals open parentheses 5 comma 3 close parentheses space dan space straight i with rightwards harpoon with barb upwards on top equals open parentheses 3 comma 4 close parentheses space maka space nilai space dari space straight k with rightwards harpoon with barb upwards on top plus straight i with rightwards harpoon with barb upwards on top plus straight m with rightwards harpoon with barb upwards on top adalah

  1. (5,3)

  2. (10,6)

  3. (15,9)

  4. (15,12)

  5. (21,1)

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell space straight k with rightwards harpoon with barb upwards on top plus straight i with rightwards harpoon with barb upwards on top plus straight m with rightwards harpoon with barb upwards on top end cell equals cell open parentheses 7 comma 2 close parentheses plus open parentheses 3 comma 4 close parentheses plus straight m with rightwards harpoon with barb upwards on top end cell row blank equals cell left parenthesis 10 comma 6 right parenthesis plus open parentheses 5 comma 3 close parentheses end cell row blank equals cell left parenthesis 15 comma 9 right parenthesis end cell end table

Oleh karena itu jawabannya adalah C

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

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

Pembahasan Soal:

Diketahui: 

begin mathsize 14px style straight a with rightwards arrow on top equals open parentheses table row 4 row 3 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 3 end table close parentheses comma space straight c with rightwards arrow on top equals open parentheses table row 1 row 5 end table close parentheses end style

Mencari begin mathsize 14px style straight a with rightwards arrow on top minus straight b with rightwards arrow on top plus straight c with rightwards arrow on top end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top minus straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell equals cell open parentheses table row 4 row 3 end table close parentheses minus open parentheses table row cell negative 2 end cell row 3 end table close parentheses plus open parentheses table row 1 row 5 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus left parenthesis negative 2 right parenthesis plus 1 end cell row cell 3 minus 3 plus 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 7 row 5 end table close parentheses end cell end table end style 

Jadi, hasil vektornya adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight a 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 straight b 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 straight c 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 7 row 5 end table close parentheses end cell end table end style.

Roboguru

Jika ,  dan  tentukan

Pembahasan Soal:

Diketahui:

Vektor begin mathsize 14px style a with rightwards arrow on top equals open square brackets table row 1 row cell negative 1 end cell end table close square brackets end stylebegin mathsize 14px style b with rightwards arrow on top equals open square brackets table row 4 row cell negative 2 end cell end table close square brackets end style dan begin mathsize 14px style c with rightwards arrow on top equals open square brackets table row cell negative 3 end cell row 3 end table close square brackets end style 

Tentukan vektor begin mathsize 14px style d with rightwards arrow on top equals a with rightwards arrow on top plus 3 b with rightwards arrow on top minus 2 c with rightwards arrow on top end style, sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell d with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus 3 b with rightwards arrow on top minus 2 c with rightwards arrow on top end cell row blank equals cell open square brackets table row 1 row cell negative 1 end cell end table close square brackets plus 3 open square brackets table row 4 row cell negative 2 end cell end table close square brackets minus 2 open square brackets table row cell negative 3 end cell row 3 end table close square brackets end cell row blank equals cell open square brackets table row 1 row cell negative 1 end cell end table close square brackets plus open square brackets table row 12 row cell negative 6 end cell end table close square brackets minus open square brackets table row cell negative 6 end cell row 6 end table close square brackets end cell row blank equals cell open square brackets table row cell 1 plus 12 minus open parentheses negative 6 close parentheses end cell row cell negative 1 plus open parentheses negative 6 close parentheses minus 6 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 1 plus 12 plus 6 end cell row cell negative 1 minus 6 minus 6 end cell end table close square brackets end cell row blank equals cell open square brackets table row 19 row cell negative 13 end cell end table close square brackets end cell end table end style

Maka, begin mathsize 14px style d with rightwards arrow on top equals open square brackets table row 19 row cell negative 13 end cell end table close square brackets end style.

Roboguru

Diketahui vektor , vektor , dan vektor . Tentukan : d.

Pembahasan Soal:

Operasi penjumlahan/pengurangan pada vektor dilakukan dengan menjumlahkan/mengurangkan elemen yang seletak, sedangkan perkalian vektor dengan skalar dilakukan dengan mengalikan skalar ke setiap elemen.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 p with rightwards arrow on top minus 2 q with rightwards arrow on top plus 2 r with rightwards arrow on top end cell equals cell 3 open parentheses table row 3 row 5 end table close parentheses minus 2 open parentheses table row 7 row cell negative 1 end cell end table close parentheses plus 2 open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell 9 minus 14 minus 8 end cell row cell 15 plus 2 plus 16 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 13 end cell row 33 end table close parentheses end cell end table end style

Jadi, hasilnya adalah begin mathsize 14px style open parentheses table row cell negative 13 end cell row 33 end table close parentheses end style.

Roboguru

Diketahui , , dan . Jika vektor satuan dari hasil  adalah , maka nilai  dan  adalah ...

Pembahasan Soal:

Diketahui  vektor begin mathsize 14px style straight a with bar on top equals open parentheses table row 3 row 11 end table close parentheses end stylebegin mathsize 14px style straight b with bar on top equals 4 straight i minus 10 straight j end style, dan begin mathsize 14px style straight c with bar on top equals 1 half straight b with bar on top end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with bar on top end cell equals cell open parentheses table row 3 row 11 end table close parentheses end cell row cell b with bar on top end cell equals cell open parentheses table row 4 row cell negative 10 end cell end table close parentheses end cell row cell c with bar on top end cell equals cell 1 half b with bar on top end cell row blank equals cell open parentheses table row 2 row cell negative 5 end cell end table close parentheses end cell row blank blank blank end table end style

Dengan menggunakan konsep penjumlahan vektor maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with bar on top plus straight b with bar on top minus straight c with bar on top end cell equals cell open parentheses table row 3 row 11 end table close parentheses plus open parentheses table row 4 row cell negative 10 end cell end table close parentheses minus open parentheses table row 2 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus 4 minus 2 end cell row cell 11 minus 10 plus 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 row 6 end table close parentheses end cell end table end style 

 Jika vektor satuan dari hasil begin mathsize 14px style a with bar on top plus b with bar on top minus c with bar on top end style adalah begin mathsize 14px style fraction numerator 1 over denominator square root of n end fraction open parentheses table row m row 6 end table close parentheses end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Vektor space satuan space straight a with bar on top plus straight b with bar on top minus straight c with bar on top end cell equals cell fraction numerator straight a with bar on top plus straight b with bar on top minus straight c with bar on top over denominator open vertical bar straight a with bar on top plus straight b with bar on top minus straight c with bar on top close vertical bar end fraction end cell row cell fraction numerator 1 over denominator square root of n end fraction open parentheses table row m row 6 end table close parentheses end cell equals cell fraction numerator open parentheses table row 5 row 6 end table close parentheses over denominator square root of 5 squared plus 6 squared end root end fraction end cell row cell fraction numerator 1 over denominator square root of n end fraction open parentheses table row m row 6 end table close parentheses end cell equals cell fraction numerator open parentheses table row 5 row 6 end table close parentheses over denominator square root of 25 plus 36 end root end fraction end cell row cell fraction numerator 1 over denominator square root of n end fraction open parentheses table row m row 6 end table close parentheses end cell equals cell fraction numerator open parentheses table row 5 row 6 end table close parentheses over denominator square root of 25 plus 36 end root end fraction end cell row cell fraction numerator 1 over denominator square root of n end fraction open parentheses table row m row 6 end table close parentheses end cell equals cell fraction numerator open parentheses table row 5 row 6 end table close parentheses over denominator square root of 61 end fraction end cell row cell fraction numerator 1 over denominator square root of n end fraction open parentheses table row m row 6 end table close parentheses end cell equals cell fraction numerator 1 over denominator square root of 61 end fraction open parentheses table row 5 row 6 end table close parentheses end cell end table end style 

Dengan demikian diperoleh nilai begin mathsize 14px style m equals 5 end style dan begin mathsize 14px style n equals 61 end style.

Oleh karena itu, jawaban yang benar adalah C. 

Roboguru

Diketahui vektor , , dan . Tentukan

Pembahasan Soal:

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

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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