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Vektor-vektor di bawah disusun membentuk persegi panjang. Nyatakanlah operasi vektor berikut ini sebagai vektor tunggal

Pertanyaan

Vektor-vektor di bawah disusun membentuk persegi panjang. Nyatakanlah operasi vektor berikut ini sebagai vektor tunggal 

begin mathsize 14px style top enclose straight p minus top enclose straight s minus top enclose straight r plus top enclose straight v end style     


 


 

Pembahasan Soal:

Perhatikan vektor-vektor tersebut pada gambar di bawah ini 


 


Berdasarkan gambar tersebut, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight p minus top enclose straight s minus top enclose straight r plus top enclose straight v end cell equals cell top enclose AB minus top enclose DA minus top enclose DC plus top enclose EB end cell row blank equals cell top enclose AB plus open parentheses negative top enclose DA close parentheses plus open parentheses negative top enclose DC close parentheses plus top enclose EB end cell row blank equals cell top enclose AB plus top enclose AD plus top enclose CD plus top enclose EB end cell row blank equals cell top enclose AB plus top enclose BC plus top enclose CD plus top enclose EB end cell row blank equals cell open parentheses top enclose AB plus top enclose BC close parentheses plus top enclose CD plus top enclose EB end cell row blank equals cell top enclose AC plus top enclose CD plus top enclose EB end cell row blank equals cell open parentheses top enclose AC plus top enclose CD close parentheses plus top enclose EB end cell row blank equals cell top enclose AD plus top enclose EB end cell row blank equals cell top enclose BC plus top enclose EB end cell row blank equals cell top enclose EB plus top enclose BC end cell row blank equals cell top enclose EC end cell row blank equals cell negative top enclose straight u end cell end table end style 

Jadi begin mathsize 14px style top enclose straight p minus top enclose straight s minus top enclose straight r plus top enclose straight v equals negative top enclose straight u end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Rante

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 31 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Vektor-vektor di bawah disusun membentuk persegi panjang. Nyatakanlah operasi vektor berikut ini sebagai vektor tunggal

Pembahasan Soal:

Perhatikan vektor-vektor tersebut pada gambar berikut


 


Berdasarkan gambar tersebut maka: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight u minus top enclose straight s plus top enclose straight v minus top enclose straight p end cell equals cell top enclose CE minus top enclose DA plus top enclose EB minus top enclose AB end cell row blank equals cell top enclose CE plus top enclose EB minus top enclose DA minus top enclose AB end cell row blank equals cell open parentheses top enclose CE plus top enclose EB close parentheses minus open parentheses top enclose DA plus AB close parentheses end cell row blank equals cell top enclose CB minus top enclose DB end cell row blank equals cell top enclose CB plus open parentheses negative top enclose DB close parentheses end cell row blank equals cell top enclose CB plus top enclose BD end cell row blank equals cell top enclose CD end cell row blank equals cell negative top enclose DC end cell row blank equals cell negative top enclose straight r end cell end table end style 

Jadi begin mathsize 14px style top enclose straight u minus top enclose straight s plus top enclose straight v minus top enclose straight p equals negative top enclose straight r end style

0

Roboguru

Vektor-vektor di bawah disusun membentuk persegi panjang. Nyatakanlah operasi vektor berikut ini sebagai vektor tunggal

Pembahasan Soal:

Perhatikan vektor-vektor tersebut pada gambar berikut


 


Berdasarkan gambar tersebut maka: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose straight r plus top enclose straight s minus top enclose straight p minus top enclose straight u minus top enclose straight v end cell equals cell top enclose DC plus top enclose DA minus top enclose AB minus top enclose CE minus top enclose EB end cell row blank equals cell top enclose DC plus top enclose CB plus open parentheses negative top enclose AB close parentheses minus top enclose CE minus top enclose EB end cell row blank equals cell open parentheses top enclose DC plus top enclose CB close parentheses plus top enclose BA minus open parentheses top enclose CE plus top enclose EB close parentheses end cell row blank equals cell top enclose DB plus top enclose BA minus top enclose CB end cell row blank equals cell open parentheses top enclose DB plus top enclose BA close parentheses minus top enclose CB end cell row blank equals cell top enclose DA minus top enclose CB end cell row blank equals cell top enclose DA minus top enclose DA end cell row blank equals 0 end table end style  

Jadi begin mathsize 14px style top enclose straight r plus top enclose straight s minus top enclose straight p minus top enclose straight u minus top enclose straight v equals 0 end style

0

Roboguru

Diketahui segitiga ABC dengan titik P di tengah AC dan Q pada BC sehingga BQ = QC. Jika   dan , maka pernyataan di bawah ini yang benar adalah ....

Pembahasan Soal:

Diketahui segitiga ABC dengan titik P di tengah AC dan Q pada BC sehingga BQ = QC. Kemudian begin mathsize 14px style AB with rightwards arrow on top equals c with italic rightwards arrow on top comma end style begin mathsize 14px style space AC with rightwards arrow on top equals b with italic rightwards arrow on top comma end style dan size 14px BC with size 14px rightwards arrow on top size 14px equals size 14px a with size 14px rightwards arrow on top. Segitiga tersebut dapat diilustrasikan sebagai berikut,

  

Kemudian, kita periksa nilai kebenaran dari masing-masing pernyataan.

1.  begin mathsize 14px style AP with rightwards arrow on top equals a with rightwards arrow on top plus 1 half b with rightwards arrow on top minus c with rightwards arrow on top end style

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AP with rightwards arrow on top end cell equals cell AQ with rightwards arrow on top minus PQ with rightwards arrow on top end cell row blank equals cell c with rightwards arrow on top plus 1 half a with rightwards arrow on top minus open curly brackets 1 half open parentheses negative a with rightwards arrow on top plus b with rightwards arrow on top close parentheses close curly brackets end cell row blank equals cell c with rightwards arrow on top minus 1 half b with rightwards arrow on top plus a with rightwards arrow on top end cell row blank equals cell a with rightwards arrow on top minus 1 half b with rightwards arrow on top plus c with rightwards arrow on top end cell end table end style 

(pernyataan 1 tidak benar)

 

2.  begin mathsize 14px style PQ with rightwards arrow on top equals 1 half open parentheses negative a with rightwards arrow on top plus b with rightwards arrow on top close parentheses end style

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with rightwards arrow on top end cell equals cell AQ with rightwards arrow on top minus AP with rightwards arrow on top end cell row blank equals cell c with rightwards arrow on top plus 1 half a with rightwards arrow on top minus 1 half b with rightwards arrow on top end cell row blank equals cell b with rightwards arrow on top minus a with rightwards arrow on top plus 1 half a with rightwards arrow on top minus 1 half b with rightwards arrow on top end cell row blank equals cell negative 1 half a with rightwards arrow on top plus 1 half b with rightwards arrow on top end cell row blank equals cell 1 half left parenthesis negative a with rightwards arrow on top plus b with rightwards arrow on top right parenthesis end cell end table end style 

(pernyataan 2 benar)

 

3.  size 14px BQ with size 14px rightwards arrow on top size 14px equals size 14px 1 over size 14px 2 begin mathsize 14px style left parenthesis negative a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top right parenthesis end style

Dapat diperhatikan bahwa begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell BQ 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 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a 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 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses b with rightwards arrow on top minus c with rightwards arrow on top close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table end style

(pernyataan 3 tidak benar)

 

4.  size 14px AQ with size 14px rightwards arrow on top size 14px equals size 14px 1 over size 14px 2 size 14px a with size 14px rightwards arrow on top size 14px plus size 14px c with size 14px rightwards arrow on top

Dapat diperhatikan bahwa begin mathsize 14px style AQ with rightwards arrow on top equals AB with rightwards arrow on top plus BQ with rightwards arrow on top equals c with italic rightwards arrow on top plus 1 half a with italic rightwards arrow on top equals 1 half a with italic rightwards arrow on top plus c with italic rightwards arrow on top. end style

(pernyataan 4 benar)

 

Pernyataan yang benar adalah pernyataan 2 dan 4.

Jadi, jawaban yang tepat adalah C. 

1

Roboguru

Diketahui P adalah titik berat ΔABC dan D adalah titik tengah BC. Jika dan maka ....

Pembahasan Soal:

Perhatikan gambar dari ΔABC berikut ini

Misalkan E dan F masing-masing merupakan titik tengah AC dan AB.

Karena D adalah titik tengah BC, maka AD, BE, dan CF merupakan garis berat ΔABC. Sehingga titik potongnya yaitu P merupakan titik berat ΔABC.

Perhatikan bahwa

begin mathsize 14px style stack P D with rightwards arrow on top equals stack B D with rightwards arrow on top minus stack B P with rightwards arrow on top end style 

Karena D adalah titik tengah BC, maka begin mathsize 14px style stack B D with rightwards arrow on top equals 1 half stack B C with rightwards arrow on top equals 1 half q with rightwards arrow on top end style

 

Kemudian karena P adalah titik berat ΔABC, maka BP : PE = 2 : 1. Sehingga begin mathsize 14px style stack B P with rightwards arrow on top equals 2 over 3 stack B E with rightwards arrow on top end style

Maka

begin mathsize 14px style stack B P with rightwards arrow on top equals 2 over 3 stack B E with rightwards arrow on top equals 2 over 3 open parentheses stack B C with rightwards arrow on top plus stack C E with rightwards arrow on top close parentheses equals 2 over 3 open parentheses q with rightwards arrow on top plus 1 half stack C A with rightwards arrow on top close parentheses equals 2 over 3 open parentheses q with rightwards arrow on top plus 1 half open parentheses stack B A with rightwards arrow on top minus stack B C with rightwards arrow on top close parentheses close parentheses equals 2 over 3 open parentheses q with rightwards arrow on top plus 1 half open parentheses p with rightwards arrow on top minus q with rightwards arrow on top close parentheses close parentheses equals 2 over 3 open parentheses q with rightwards arrow on top plus 1 half p with rightwards arrow on top minus 1 half q with rightwards arrow on top close parentheses equals 2 over 3 open parentheses 1 half p with rightwards arrow on top plus 1 half q with rightwards arrow on top close parentheses equals 1 third p with rightwards arrow on top plus 1 third q with rightwards arrow on top end style  

Sehingga

begin mathsize 14px style stack P D with rightwards arrow on top equals stack B D with rightwards arrow on top minus stack B P with rightwards arrow on top equals 1 half q with rightwards arrow on top minus open parentheses 1 third p with rightwards arrow on top plus 1 third q with rightwards arrow on top close parentheses equals 1 half q with rightwards arrow on top minus 1 third p with rightwards arrow on top minus 1 third q with rightwards arrow on top equals negative 1 third p with rightwards arrow on top plus 1 half q with rightwards arrow on top minus 1 third q with rightwards arrow on top equals negative 1 third p with rightwards arrow on top plus 3 over 6 q with rightwards arrow on top minus 2 over 6 q with rightwards arrow on top equals negative 1 third p with rightwards arrow on top plus 1 over 6 q with rightwards arrow on top end style 

 

 

0

Roboguru

Diketahui :   Nyatakan sebagai vektor kolom! e.

Pembahasan Soal:

Pembahasan:

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

 

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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