Roboguru

Diketahui vektor  dan  serta vektor  tegak lurus terhadap vektor . hitunglah nilai p yang mungkin!

Pertanyaan

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 4 row 2 row cell negative 3 end cell end table close parentheses end style dan begin mathsize 14px style b with rightwards arrow on top equals open parentheses table row p row 3 row 6 end table close parentheses end style serta vektor begin mathsize 14px style a with rightwards arrow on top end style tegak lurus terhadap vektor begin mathsize 14px style b with rightwards arrow on top end style. hitunglah nilai p yang mungkin!

Pembahasan Soal:

Karena vektor begin mathsize 14px style a with rightwards arrow on top end style tegak lurus terhadap vektor begin mathsize 14px style b with rightwards arrow on top end style maka

 begin mathsize 14px style a with rightwards arrow on top space times space b with rightwards arrow on top equals 0 open parentheses table row 4 row 2 row cell negative 3 end cell end table close parentheses times open parentheses table row p row 3 row 6 end table close parentheses equals 0 4 p plus 6 minus 18 equals 0 4 p minus 12 equals 0 4 p equals 12 p equals 3 end style 

Jadi, nilai p = 3

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 28 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui koordinat titik , , dan . Hasil perkalian  adalah ....

Pembahasan Soal:

Gunakan konsep dot produk pada vektor.

Diketahui koordinat titik straight P open parentheses 3 comma space minus 1 comma space 4 close parenthesesstraight Q open parentheses negative 2 comma space 1 comma space minus 5 close parentheses, dan straight R open parentheses 4 comma space 3 comma space minus 2 close parentheses. Akan ditentukan hasil perkalian PQ with rightwards arrow on top times PR with rightwards arrow on top.

*Menentukan PQ with rightwards arrow on top.

table attributes columnalign right center left columnspacing 2px end attributes row cell PQ with rightwards arrow on top end cell equals cell straight Q minus straight P end cell row blank equals cell open parentheses table row cell negative 2 end cell row 1 row cell negative 5 end cell end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 minus 3 end cell row cell 1 minus open parentheses negative 1 close parentheses end cell row cell negative 5 minus 4 end cell end table close parentheses end cell row cell PQ with rightwards arrow on top end cell equals cell open parentheses table row cell negative 5 end cell row 2 row cell negative 9 end cell end table close parentheses end cell end table

*Menentukan PR with rightwards arrow on top.

table attributes columnalign right center left columnspacing 2px end attributes row cell PR with rightwards arrow on top end cell equals cell straight R minus straight P end cell row blank equals cell open parentheses table row 4 row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 3 end cell row cell 3 minus open parentheses negative 1 close parentheses end cell row cell negative 2 minus 4 end cell end table close parentheses end cell row cell PR with rightwards arrow on top end cell equals cell open parentheses table row 1 row 4 row cell negative 6 end cell end table close parentheses end cell end table

Sehingga nilai PQ with rightwards arrow on top times PR with rightwards arrow on top dapat dihitung sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell PQ with rightwards arrow on top times PR with rightwards arrow on top end cell equals cell open parentheses table row cell negative 5 end cell row 2 row cell negative 9 end cell end table close parentheses times open parentheses table row 1 row 4 row cell negative 6 end cell end table close parentheses end cell row blank equals cell open parentheses negative 5 close parentheses open parentheses 1 close parentheses plus open parentheses 2 close parentheses open parentheses 4 close parentheses plus open parentheses negative 9 close parentheses open parentheses negative 6 close parentheses end cell row blank equals cell negative 5 plus 8 plus 54 end cell row cell PQ with rightwards arrow on top times PR with rightwards arrow on top end cell equals 57 end table

Diperoleh hasil perkalian PQ with rightwards arrow on top times PR with rightwards arrow on top adalah 57.

Jadi, tidak ada jawaban yang tepat.

Roboguru

Diketahui vektor , , dan . Tentukan hasil dari: c.

Pembahasan Soal:

Dengan menerapkan konsep perkalian vektor dot product, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell q with rightwards arrow on top times r with rightwards arrow on top end cell equals cell open parentheses negative 1 close parentheses open parentheses 2 close parentheses plus open parentheses 3 close parentheses open parentheses 1 close parentheses end cell row blank equals cell negative 2 plus 3 end cell row blank equals 1 end table end style 

Selanjutnya, dengan menerapkan perkalian skalar dengan vektor diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top open parentheses q with rightwards arrow on top times r with rightwards arrow on top close parentheses end cell equals cell p with rightwards arrow on top times open parentheses 1 close parentheses end cell row blank equals cell p with rightwards arrow on top end cell row blank equals cell negative 4 i with rightwards arrow on top minus 7 j with rightwards arrow on top end cell end table end style 

Dengan demikian, hasil dari begin mathsize 14px style p with rightwards arrow on top open parentheses q with rightwards arrow on top times r with rightwards arrow on top close parentheses end style adalah begin mathsize 14px style negative 4 i with rightwards arrow on top minus 7 j with rightwards arrow on top end style.

Roboguru

Diketahui , , dan . Jika . Maka nilai x adalah ....

Pembahasan Soal:

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell space i minus 3 j plus 2 k rightwards arrow open parentheses 1 comma space minus 3 comma space 2 close parentheses end cell row cell b with rightwards arrow on top end cell equals cell 2 i plus 8 j plus 2 k rightwards arrow open parentheses 2 comma space 8 comma space 2 close parentheses end cell row cell c with rightwards arrow on top end cell equals cell 8 j plus x k rightwards arrow open parentheses 0 comma space 8 comma space x close parentheses end cell end table 

Untuk menyelesaikan soal tersebut, terlebih dahulu dicari hasil dari open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell open parentheses 2 plus 0 close parentheses i plus open parentheses 8 plus 8 close parentheses j plus open parentheses 2 plus x close parentheses k end cell row cell open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell 2 i plus 16 j plus open parentheses 2 plus x close parentheses k end cell row cell open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell open parentheses 2 comma space 16 comma space open parentheses 2 plus x close parentheses close parentheses end cell row blank blank blank end table 

Sehingga diperoleh, perkalian (dot) vektor sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell a with rightwards arrow on top times a with rightwards arrow on top end cell row cell open parentheses 1 cross times 2 close parentheses plus open parentheses open parentheses negative 3 close parentheses cross times 16 close parentheses plus open parentheses 2 open parentheses 2 plus x close parentheses close parentheses end cell equals cell open parentheses 1 cross times 1 close parentheses plus open parentheses open parentheses negative 3 close parentheses cross times open parentheses negative 3 close parentheses close parentheses plus open parentheses 2 cross times 2 close parentheses end cell row cell 2 minus 48 plus 4 plus 2 x end cell equals cell 1 plus 9 plus 4 end cell row cell negative 42 plus 2 x end cell equals 14 row cell 2 x end cell equals cell 14 plus 42 end cell row cell 2 x end cell equals 56 row x equals cell 56 over 2 end cell row x equals 28 end table 

Oleh karena itu, jawaban yang benar adalah D.

Roboguru

Jika vektor  dan  hasil ...

Pembahasan Soal:

Jika vektor a with bar on top equals 4 i with bar on top minus 5 j with bar on top dan b with bar on top equals i with bar on top plus 6 j with bar on top, berdasarkan operasi dot product maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with bar on top times b with bar on top end cell equals cell open parentheses 4 comma space minus 5 close parentheses times open parentheses 1 comma space 6 close parentheses end cell row blank equals cell open parentheses 4 times 1 close parentheses plus open parentheses negative 5 times 6 close parentheses end cell row blank equals cell 4 minus 30 end cell row blank equals cell negative 26 end cell end table 

Oleh karena itu jawaban yang benar adalah E.

Roboguru

1. Diketahui vektor-vektor  Tentukan: a.  a∙b

Pembahasan Soal:

begin mathsize 14px style a with rightwards harpoon with barb upwards on top bullet b with rightwards arrow on top equals open parentheses stack a subscript i with rightwards arrow on top cross times b with rightwards arrow on top subscript i close parentheses plus open parentheses a with rightwards arrow on top subscript j cross times b with rightwards arrow on top subscript j close parentheses a with rightwards arrow on top bullet b with rightwards arrow on top equals open parentheses 2 cross times 6 close parentheses plus open parentheses negative 1 cross times negative 2 close parentheses a with rightwards arrow on top bullet b with rightwards arrow on top equals 12 plus 2 a with rightwards arrow on top bullet b with rightwards arrow on top equals 14 end style 

Dengan demikian, nilai ab adalah 14.

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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