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O adalah titik awal. Jika  adalah vektor posisi P,  adalah vektor posisi Q dan  adalah vektor posisi R, ;  dan , maka vektor posisi titik U adalah ...

Pertanyaan

O adalah titik awal. Jika straight p with rightwards arrow on top adalah vektor posisi P, straight q with rightwards arrow on top adalah vektor posisi Q dan straight r with rightwards arrow on top adalah vektor posisi R, RS with rightwards arrow on top equals straight q with rightwards arrow on topQT with rightwards arrow on top equals straight p with rightwards arrow on top dan SU with rightwards arrow on top equals OT with rightwards arrow on top, maka vektor posisi titik U adalah ...

  1. negative straight p with rightwards arrow on top minus 2 straight q with rightwards arrow on top minus straight r with rightwards arrow on top

  2. straight p with rightwards arrow on top minus 2 straight q with rightwards arrow on top minus straight r with rightwards arrow on top

  3. negative straight p with rightwards arrow on top plus 2 straight q with rightwards arrow on top minus straight r with rightwards arrow on top

  4. straight p with rightwards arrow on top plus 2 straight q with rightwards arrow on top plus straight r with rightwards arrow on top

  5. negative straight p with rightwards arrow on top plus 2 straight q with rightwards arrow on top minus straight r with rightwards arrow on top

Pembahasan Soal:

Ingatlah bahwa Vektor Posisi adalah vektor yang berpangkal di pusat koordinat straight O open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik misalkan straight A open parentheses straight x comma space straight y close parentheses. Notasi vektor posisi adalah OA with rightwards arrow on top.

Selanjutnya, mIsalkan terdapat dua buah vektor posisi OA with rightwards arrow on top equals straight a with rightwards arrow on top dan OB with rightwards arrow on top equals straight b with rightwards arrow on top. Vektor AB dapat didefinisikan sebagai:

AB with rightwards arrow on top equals OB with rightwards arrow on top minus OA with rightwards arrow on top equals straight b with rightwards arrow on top minus straight a with rightwards arrow on top.

Diketahui vektor posisi:

  • OP with rightwards arrow on top equals straight p with rightwards arrow on top
  • OQ with rightwards arrow on top equals straight q with rightwards arrow on top
  • OR with rightwards arrow on top equals straight r with rightwards arrow on top
  • OS with rightwards arrow on top equals straight s with rightwards arrow on top
  • RS with rightwards arrow on top equals straight q with rightwards arrow on top maka straight s with rightwards arrow on top minus straight r with rightwards arrow on top equals straight q with rightwards arrow on top rightwards arrow straight s with rightwards arrow on top equals straight q with rightwards arrow on top plus straight r with rightwards arrow on top
  • QT with rightwards arrow on top equals straight p with rightwards arrow on top maka straight t with rightwards arrow on top minus straight q with rightwards arrow on top equals straight p with rightwards arrow on top rightwards arrow straight t with rightwards arrow on top equals straight p with rightwards arrow on top plus straight q with rightwards arrow on top
  • SU with rightwards arrow on top equals OT with rightwards arrow on top

Pada soal diketahui SU with rightwards arrow on top equals OT with rightwards arrow on top, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell SU with rightwards arrow on top end cell equals cell OT with rightwards arrow on top end cell row cell straight u with rightwards arrow on top minus straight s with rightwards arrow on top end cell equals cell straight t with rightwards arrow on top end cell row cell straight u with rightwards arrow on top end cell equals cell straight t with rightwards arrow on top plus straight s with rightwards arrow on top end cell row cell straight u with rightwards arrow on top end cell equals cell straight p with rightwards arrow on top plus straight q with rightwards arrow on top plus straight q with rightwards harpoon with barb upwards on top plus straight r with rightwards harpoon with barb upwards on top end cell row cell straight u with rightwards arrow on top end cell equals cell straight p with rightwards arrow on top plus 2 straight q with rightwards harpoon with barb upwards on top plus straight r with rightwards harpoon with barb upwards on top end cell end table

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight u with rightwards arrow on top end cell end table sama dengan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight u 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 straight p 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight q 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 plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight r with rightwards harpoon with barb upwards on top end cell end table.

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Nuryani

Mahasiswa/Alumni Universitas Padjadjaran

Terakhir diupdate 11 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui koordinat titik , , dan . Jika vektor , koordinat titik adalah

Pembahasan Soal:

Diketahui koordinat titik straight P left parenthesis negative 1 comma negative 3 right parenthesis, straight Q left parenthesis 3 comma negative 2 right parenthesis, dan straight R left parenthesis 2 comma 3 right parenthesis. Diketahui juga vektor PQ with bar on top equals RS with bar on top.

Perhatikan bahwa vektor

PQ with bar on top equals q with bar on top minus p with bar on top

dan

RS with bar on top equals r with bar on top minus s with bar on top

dengan p with bar on top comma space q with bar on top comma space r with bar on top comma space dan space s with bar on top masing-masing adalah vektor posisi titik P comma space Q comma space R comma space dan space S.

Karena PQ with bar on top equals RS with bar on top, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell q with bar on top minus p with bar on top end cell equals cell s with bar on top minus r with bar on top end cell row cell q with bar on top minus p with bar on top plus r with bar on top end cell equals cell s with bar on top end cell row cell open parentheses table row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row cell negative 3 end cell end table close parentheses plus open parentheses table row 2 row 3 end table close parentheses end cell equals cell s with bar on top end cell row cell open parentheses table row cell 3 minus open parentheses negative 1 close parentheses plus 2 end cell row cell open parentheses negative 2 close parentheses minus open parentheses negative 3 close parentheses plus 3 end cell end table close parentheses end cell equals cell s with bar on top end cell row cell open parentheses table row cell 3 plus 1 plus 2 end cell row cell open parentheses negative 2 close parentheses plus 3 plus 3 end cell end table close parentheses end cell equals cell s with bar on top end cell row cell open parentheses table row 6 row 4 end table close parentheses end cell equals cell s with bar on top end cell end table

Koordinat titik straight S sama nilainya dengan vektor posisi s with bar on top. Dengan demikian, koordinat titik straight S adalah open parentheses 6 comma space 4 close parentheses.

0

Roboguru

Gambarlah titik-titik berikut:

Pembahasan Soal:

Gambar yang sesuai :

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Roboguru

Diketahui vektor  dan . Jika  maka koordinat titik B adalah ...

Pembahasan Soal:

Diketahui vektor stack A B with rightwards arrow on top equals open parentheses table row 3 row 1 end table close parenthesesstack A C with rightwards arrow on top equals open parentheses table row 5 row 2 end table close parentheses dan straight C left parenthesis 4 comma space 6 right parenthesis atau dapat ditulis dalam bentuk vektor posisi menjadi stack O C with rightwards arrow on top equals open parentheses table row 4 row 6 end table close parentheses.

Ingat!

Pada vektor, stack A B with rightwards arrow on top didefinisikan dengan stack A B with rightwards arrow on top equals stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top.

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A C with rightwards arrow on top end cell equals cell stack O C with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row cell stack O A with rightwards arrow on top end cell equals cell stack O C with rightwards arrow on top minus stack A C with rightwards arrow on top end cell row blank equals cell open parentheses table row 4 row 6 end table close parentheses minus open parentheses table row 5 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 5 end cell row cell 6 minus 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row blank blank blank row cell stack A B with rightwards arrow on top end cell equals cell stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row cell stack A B with rightwards arrow on top plus stack O A with rightwards arrow on top end cell equals cell stack O B with rightwards arrow on top end cell row cell stack O B with rightwards arrow on top end cell equals cell stack A B with rightwards arrow on top plus stack O A with rightwards arrow on top end cell row blank equals cell open parentheses table row 3 row 1 end table close parentheses plus open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus left parenthesis negative 1 right parenthesis end cell row cell 1 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row 5 end table close parentheses end cell end table 

Koordinat titik B akan bernilai sama dengan vektor posisi stack O B with rightwards arrow on top, sehingga koordinat titik B adalah left parenthesis 2 comma space 5 right parenthesis.

Jadi, jawaban yang tepat adalah E.

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Roboguru

Pada jajargenjang ABCD diketahui vektor posisi ,  dan  dengan demikian koordinat titik B adalah ...

Pembahasan Soal:

Diketahui jajargenjang ABCD yang tersusun dari vektor posisi a with bar on top equals open parentheses table row 2 row cell negative 2 end cell end table close parenthesesc with bar on top equals open parentheses table row cell negative 4 end cell row 3 end table close parentheses dan d with bar on top equals open parentheses table row 1 row 2 end table close parentheses.

Ingat!

Pada vektor, stack A B with rightwards arrow on top didefinisikan dengan stack A B with rightwards arrow on top equals stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top.

Maka:

Pada jajargenjang ABCD, AB sejajar dan searah dengan DC, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell stack D C with rightwards arrow on top end cell row cell b with rightwards arrow on top minus a with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus d with rightwards arrow on top end cell row cell b with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus c with rightwards arrow on top minus d with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row cell negative 2 end cell end table close parentheses plus open parentheses table row cell negative 4 end cell row 3 end table close parentheses minus open parentheses table row 1 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus left parenthesis negative 4 right parenthesis end cell row cell negative 2 plus 3 end cell end table close parentheses minus open parentheses table row 1 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row 1 end table close parentheses minus open parentheses table row 1 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 minus 1 end cell row cell 1 minus 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row cell negative 1 end cell end table close parentheses end cell end table 

Koordinat titik B akan bernilai sama dengan vektor posisi b with rightwards arrow on top, sehingga koordinat titik B adalah left parenthesis negative 3 comma space minus 1 right parenthesis

Jadi, jawaban yang tepat adalah B. 

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Roboguru

Misal diketahui ,  dan . Jika  dan  searah dengan  maka koordinat titik adalah ...

Pembahasan Soal:

Diketahui  PQ with bar on top searah dengan RS with bar on top maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with bar on top end cell equals cell stack italic R S with bar on top end cell row cell italic Q minus sign P end cell equals cell S minus sign italic R end cell row S equals cell italic Q minus sign P and italic R end cell row blank equals cell open parentheses 7 comma space 1 comma space 2 close parentheses minus sign open parentheses 3 comma space 5 comma space 4 close parentheses plus open parentheses 4 comma space 3 comma space 1 close parentheses end cell row blank equals cell open parentheses 7 minus sign 3 plus 4 comma space 1 minus sign 5 plus 3 comma space 2 minus sign 4 plus 1 close parentheses end cell row blank equals cell open parentheses 8 comma space minus sign 1 comma space minus sign 1 close parentheses end cell end table 

Maka koordinat titik S spaceadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 8 comma space minus sign 1 comma space minus sign 1 close parentheses end cell end table.

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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