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Diketahui koordinat titik , , , dan . Jika hasil dari , maka nilai n adalah ...

Pertanyaan

Diketahui koordinat titik straight A left parenthesis 4 comma 2 right parenthesis, straight B left parenthesis 2 comma 5 right parenthesis, straight C left parenthesis 1 comma 5 right parenthesis, dan straight D left parenthesis 8 comma 4 right parenthesis. Jika hasil dari 3 stack A B with rightwards arrow on top plus 2 stack D B with rightwards arrow on top minus stack D C with rightwards arrow on top equals open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses, maka nilai n adalah ...

  1. 13

  2. 12

  3. 11

  4. 10

  5. 9

Pembahasan Soal:

Ingat bagaimana cara menentukan suatu vektor dengan titik yang diketahui dan ingat operasi perkalian skalar dengan vektor serta operasi penjumlahan dan pengurangan vektor.

Menentukan vektor-vektor

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 minus A end cell row blank equals cell open parentheses 2 , 5 close parentheses minus left parenthesis 4 , 2 right parenthesis end cell row blank equals cell left parenthesis negative 2 , 3 right parenthesis end cell row blank blank blank row cell stack D B with rightwards arrow on top end cell equals cell B minus D end cell row blank equals cell open parentheses 2 , 5 close parentheses minus left parenthesis 8 , 4 right parenthesis end cell row blank equals cell left parenthesis negative 6 , 1 right parenthesis end cell row blank blank blank row cell stack D C with rightwards arrow on top end cell equals cell C minus D end cell row blank equals cell open parentheses 1 , 5 close parentheses minus left parenthesis 8 , 4 right parenthesis end cell row blank equals cell open parentheses negative 7 , 1 close parentheses end cell end table

Menentukan nilai n

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 stack A B with rightwards arrow on top plus 2 stack D B with rightwards arrow on top minus stack D C with rightwards arrow on top end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell 3 left parenthesis negative 2 , 3 right parenthesis plus 2 left parenthesis negative 6 , 1 right parenthesis minus open parentheses negative 7 , 1 close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell 3 open parentheses table row cell negative 2 end cell row 3 end table close parentheses plus 2 open parentheses table row cell negative 6 end cell row 1 end table close parentheses minus open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell open parentheses table row cell negative 6 end cell row 9 end table close parentheses plus open parentheses table row cell negative 12 end cell row 2 end table close parentheses minus open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell open parentheses table row cell negative 18 end cell row 11 end table close parentheses minus open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell open parentheses table row cell negative 11 end cell row 10 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell end table

dari hasil di atas didapatkan 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative n end cell equals cell negative 11 end cell row n equals 11 end table

Diperoleh n equals 11.

Jadi, dapat disimpulkan bahwa nilai dari n adalah 11.

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika , dan , maka vektor satuan adalah ...

Pembahasan Soal:

Vektor satuan dari vektor dua dimensi straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell end table close parentheses adalah sebagai berikut.

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 equals fraction numerator open parentheses straight a subscript 1 comma space straight a subscript 2 close parentheses over denominator square root of straight a subscript 1 squared plus straight a subscript 2 squared end root end fraction.

Sebelum mencari vektor satuan dari straight d with rightwards arrow on top, hitunglah operasi vektornya terlebih dahulu, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards arrow on top end cell equals cell 2 straight a with rightwards arrow on top minus 2 straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell row cell straight d with rightwards arrow on top end cell equals cell 2 open parentheses table row 1 row 5 end table close parentheses minus 2 open parentheses table row 4 row 5 end table close parentheses plus open parentheses table row 0 row 8 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 2 row 10 end table close parentheses minus open parentheses table row 8 row 10 end table close parentheses plus open parentheses table row 0 row 8 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell 2 minus 8 plus 0 end cell row cell 10 minus 10 plus 8 end cell end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell negative 6 end cell row 8 end table close parentheses end cell end table

Selanjutnya, vektor satuan straight d with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d with rightwards arrow on top over denominator open vertical bar straight d with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator square root of open parentheses negative 6 close parentheses squared plus 8 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator square root of 36 plus 64 end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator square root of 100 end fraction end cell row blank equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator 10 end fraction end cell row blank equals cell 1 over 10 open parentheses table row cell negative 6 end cell row 8 end table close parentheses end cell end table

Dengan demikian, jawaban yang benar adalah C.

0

Roboguru

Diketahui vektor , , dan . Vektor  sama dengan ...

Pembahasan Soal:

Ingat operasi penjumlahan dan pengurangan vektor dengan jenis vektor kolom, sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 u with rightwards arrow on top plus 2 v with rightwards arrow on top minus w with rightwards arrow on top end cell equals cell 3 open parentheses table row 3 row 2 row cell negative 4 end cell end table close parentheses plus 2 open parentheses table row cell negative 1 end cell row 5 row 2 end table close parentheses minus open parentheses table row 4 row cell negative 1 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 9 row 6 row cell negative 12 end cell end table close parentheses plus open parentheses table row cell negative 2 end cell row 10 row 4 end table close parentheses minus open parentheses table row 4 row cell negative 1 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 7 row 16 row cell negative 8 end cell end table close parentheses minus open parentheses table row 4 row cell negative 1 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 17 row cell negative 9 end cell end table close parentheses end cell end table

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Diketahui  dan  dengan  dan  konstanta serta vektor  dan  dua vektor tidak saling sejajar. Jika . Nilai  adalah ...

Pembahasan Soal:

Diketahui a with rightwards arrow on top equals 2 p with rightwards arrow on top plus q with rightwards arrow on top dan b with rightwards arrow on top equals p with rightwards arrow on top minus 4 q with rightwards arrow on top, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell 2 open parentheses 2 p with rightwards arrow on top plus q with rightwards arrow on top close parentheses minus 2 open parentheses p with rightwards arrow on top minus 4 q with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 4 p with rightwards arrow on top plus 2 q with rightwards arrow on top close parentheses minus open parentheses 2 p with rightwards arrow on top minus 8 q with rightwards arrow on top close parentheses end cell row blank equals cell 4 p with rightwards arrow on top minus 2 p with rightwards arrow on top plus 2 q with rightwards arrow on top plus 8 q with rightwards arrow on top end cell row blank equals cell 2 p with rightwards arrow on top plus 10 q with rightwards arrow on top space end cell end table

Diketahui pula c with rightwards arrow on top equals m p with rightwards arrow on top plus open parentheses m plus n minus 1 close parentheses q with rightwards arrow on top dan c with rightwards arrow on top equals 2 a with rightwards arrow on top minus 2 b with rightwards arrow on top, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell 2 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell row cell m p with rightwards arrow on top plus open parentheses m plus n minus 1 close parentheses q with rightwards arrow on top end cell equals cell 2 p with rightwards arrow on top plus 10 q with rightwards arrow on top space end cell row blank blank blank end table 

Dari kesamaan vektor tersebut diperoleh 

m equals 2 space dan space m plus n minus 1 equals 10 

Substitusi m equals 2 ke m plus n minus 1 equals 10, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell m plus n minus 1 end cell equals 10 row cell 2 plus n minus 1 end cell equals 10 row cell 1 plus n end cell equals 10 row n equals 9 end table 

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell m plus n end cell equals cell 2 plus 9 end cell row blank equals 11 end table 

Jadi, nilai open parentheses m plus n close parentheses adalah 9

0

Roboguru

Diketahui , , dan . Jika , panjang vektor  adalah ....

Pembahasan Soal:

Dengan menerapkan konsep penjumlahan vektor dan perkalian vektor dengan skalar, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top end cell equals cell u with rightwards arrow on top minus 2 v with rightwards arrow on top plus 3 w with rightwards arrow on top end cell row blank equals cell u with rightwards arrow on top plus open parentheses negative 2 v with rightwards arrow on top close parentheses plus 3 w with rightwards arrow on top end cell row blank equals cell open parentheses table row 4 row cell negative 5 end cell row 3 end table close parentheses plus open parentheses negative 2 close parentheses open parentheses table row 2 row 2 row 1 end table close parentheses plus 3 open parentheses table row 4 row 1 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 5 end cell row 3 end table close parentheses plus open parentheses table row cell negative 4 end cell row cell negative 4 end cell row cell negative 2 end cell end table close parentheses plus open parentheses table row 12 row 3 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 12 row cell negative 6 end cell row cell negative 2 end cell end table close parentheses end cell end table end style 

Selanjutnya, dengan menerapkan rumus panjang vektor pada tiga dimensi, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell square root of 12 squared plus open parentheses negative 6 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 144 plus 36 plus 4 end root end cell row blank equals cell square root of 184 end cell row blank equals cell square root of 4 cross times 46 end root end cell row blank equals cell 2 square root of 46 end cell end table end style 

Dengan demikian, panjang vektor size 14px p with size 14px rightwards arrow on top adalah begin mathsize 14px style 2 square root of 46 end style.

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Diketahui vektor-vektor , , dan . Vektor . Dalam bentuk vektor basis adalah ....

Pembahasan Soal:

Diketahui vektor-vektor p with bar on top equals open parentheses table row 4 row cell negative 2 end cell end table close parenthesesq with bar on top equals open parentheses table row 9 row cell negative 6 end cell end table close parentheses, dan r with bar on top equals open parentheses table row 4 row 6 end table close parentheses. Vektor s with bar on top equals 1 half p with bar on top minus 1 third q with bar on top plus 1 fourth r with bar on top dapat dinyatakan sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell s with bar on top end cell equals cell 1 half open parentheses table row 4 row cell negative 2 end cell end table close parentheses minus 1 third open parentheses table row 9 row cell negative 6 end cell end table close parentheses plus 1 fourth open parentheses table row 4 row 6 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 minus open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row 1 row cell 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 minus 3 plus 1 end cell row cell negative 1 plus 2 plus 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell 4 over 4 plus 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell 10 over 4 end cell end table close parentheses end cell row blank equals cell negative 10 over 4 j end cell end table

Jadi, s with bar on top equals negative 10 over 4 j.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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