Roboguru

Diketahui x⇀=(6,4), y⇀​=(2,5) dan z⇀=(−1,3). Tentukan xy⇀​−xz⇀.

Pertanyaan

Diketahui begin mathsize 14px style x with rightwards harpoon with barb upwards on top equals left parenthesis 6 comma 4 right parenthesis end stylebegin mathsize 14px style y with rightwards harpoon with barb upwards on top equals left parenthesis 2 comma 5 right parenthesis end style dan begin mathsize 14px style z with rightwards harpoon with barb upwards on top equals left parenthesis negative 1 comma 3 right parenthesis end style. Tentukan begin mathsize 14px style stack x y with rightwards harpoon with barb upwards on top minus stack x z with rightwards harpoon with barb upwards on top end style.

Pembahasan Soal:

Diketahui begin mathsize 14px style x with rightwards harpoon with barb upwards on top equals left parenthesis 6 comma 4 right parenthesis end stylebegin mathsize 14px style y with rightwards harpoon with barb upwards on top equals left parenthesis 2 comma 5 right parenthesis end style dan begin mathsize 14px style z with rightwards harpoon with barb upwards on top equals left parenthesis negative 1 comma 3 right parenthesis end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack x y with rightwards harpoon with barb upwards on top minus stack x z with rightwards harpoon with barb upwards on top end cell equals cell open parentheses y with rightwards harpoon with barb upwards on top minus x with rightwards harpoon with barb upwards on top close parentheses minus open parentheses z with rightwards harpoon with barb upwards on top minus x with rightwards harpoon with barb upwards on top close parentheses end cell row blank equals cell y with rightwards harpoon with barb upwards on top minus x with rightwards harpoon with barb upwards on top minus z with rightwards harpoon with barb upwards on top plus x with rightwards harpoon with barb upwards on top end cell row blank equals cell y with rightwards harpoon with barb upwards on top minus z with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses 2 comma 5 close parentheses minus open parentheses negative 1 comma 3 close parentheses end cell row blank equals cell open parentheses 3 comma 2 close parentheses end cell end table end style 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Sri

Mahasiswa/Alumni Universitas Muhammadiyah Purworejo

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui titik A(−4,7) dan B(−3,−1). Tentukan vektor : b. BA

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BA with rightwards arrow on top end cell equals cell straight A minus straight B end cell row blank equals cell open parentheses table row cell negative 4 end cell row 7 end table close parentheses minus open parentheses table row cell negative 3 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 8 end table close parentheses end cell end table end style  

Sehingga, begin mathsize 14px style BA with rightwards arrow on top equals open parentheses negative 1 comma 8 close parentheses end style.

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Roboguru

Tuliskan dalam bentuk vektor kolom dan kombinasi linear dari vektor AB jika: b. A(2,1) dan B(−9,3)

Pembahasan Soal:

Pertama, dalam bentuk vektor kolom sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row cell negative 9 end cell row 3 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 11 end cell row 2 end table close parentheses end cell end table end style   

Kedua,bentuk kombinasi linear sebagai berikut:

begin mathsize 14px style AB with rightwards arrow on top equals open parentheses table row cell negative 11 end cell row 2 end table close parentheses equals open parentheses negative 11 comma 2 close parentheses equals negative 11 straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top end style 

Sehingga, vektor kolom undefined adalah begin mathsize 14px style open parentheses table row cell negative 11 end cell row 2 end table close parentheses end style dan bentuk kombinasi linearnya adalah begin mathsize 14px style negative 11 straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top end style.

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Roboguru

Diketahui titik A(−4,7) dan B(−3,−1). Tentukan vektor : a. AB

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A 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 minus open parentheses table row cell negative 4 end cell row 7 end table close parentheses end cell row blank equals cell open parentheses table row 1 row cell negative 8 end cell end table close parentheses end cell end table end style 

Sehingga, begin mathsize 14px style AB with rightwards arrow on top equals open parentheses 1 comma negative 8 close parentheses end style.

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Roboguru

Diketahui koordinat titik P(4,7,−2),Q(2,−3,5), dan R(−1,4,0). Tentukan: b. koordinat S sehingga PS=3PR−PQ​

Pembahasan Soal:

Vektor posisi adalah vektor yang berpangkal di koordinat titik begin mathsize 14px style open parentheses x subscript 1 comma space y subscript 1 close parentheses end style dan berujung di suatu titik begin mathsize 14px style open parentheses x subscript 2 comma space y subscript 2 close parentheses end style. Cara menentukan vektor posisi yaitu dengan menghitung selisih dari koordinat titik ujung dan titik pangkal.

Koordinat titik P akan sama nilainya dengan vektor posisi begin mathsize 14px style p with rightwards arrow on top end style. Hal ini berlaku pula untuk koordinat titik Q, R, dan S.

Pada persamaan begin mathsize 14px style PS with rightwards arrow on top equals 3 PR with rightwards arrow on top minus PQ with rightwards arrow on top end style terdapat vektor posisi, perkalian vektor dengan skalar, dan selisih dua vektor posisi, Sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell PS with rightwards arrow on top end cell equals cell 3 PR with rightwards arrow on top minus PQ with rightwards arrow on top end cell row cell s with rightwards arrow on top minus p with rightwards arrow on top end cell equals cell 3 open parentheses r with rightwards arrow on top minus p with rightwards arrow on top close parentheses minus open parentheses q with rightwards arrow on top minus p with rightwards arrow on top close parentheses end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell 3 times open square brackets open parentheses table row cell negative 1 end cell row 4 row 0 end table close parentheses minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses close square brackets minus open square brackets open parentheses table row 2 row cell negative 3 end cell row 5 end table close parentheses minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses close square brackets end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell 3 times open parentheses table row cell negative 5 end cell row cell negative 3 end cell row 2 end table close parentheses minus open parentheses table row cell negative 2 end cell row cell negative 10 end cell row 7 end table close parentheses end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 15 end cell row cell negative 9 end cell row 6 end table close parentheses minus open parentheses table row cell negative 2 end cell row cell negative 10 end cell row 7 end table close parentheses end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 13 end cell row 1 row cell negative 1 end cell end table close parentheses end cell row cell s with rightwards arrow on top end cell equals cell open parentheses table row cell negative 13 end cell row 1 row cell negative 1 end cell end table close parentheses plus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell row cell s with rightwards arrow on top end cell equals cell open parentheses table row cell negative 9 end cell row 8 row cell negative 3 end cell end table close parentheses end cell row blank blank blank end table end style 

Jadi, koordinat titik begin mathsize 14px style straight S left parenthesis negative 9 comma space 8 comma space minus 3 right parenthesis end style.

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Roboguru

Tuliskan dalam bentuk vektor kolom dan kombinasi linear dari vektor AB jika: a. A(−4,3) dan B(2,−7)

Pembahasan Soal:

Pertama, dalam bentuk vektor kolom sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 2 row cell negative 7 end cell end table close parentheses minus open parentheses table row cell negative 4 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 10 end cell end table close parentheses end cell end table end style  

Kedua,bentuk kombinasi linear sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell open parentheses negative 4 comma 3 close parentheses equals negative 4 straight i with rightwards arrow on top plus 3 straight j with rightwards arrow on top end cell row straight B equals cell open parentheses 2 comma negative 7 close parentheses equals 2 straight i with rightwards arrow on top minus 7 straight j with rightwards arrow on top end cell end table end style 

begin mathsize 14px style AB with rightwards arrow on top equals open parentheses 6 comma negative 10 close parentheses equals 6 straight i with rightwards arrow on top minus 10 straight j with rightwards arrow on top end style 

Sehingga, vektor kolom undefined adalah begin mathsize 14px style open parentheses table row 6 row cell negative 10 end cell end table close parentheses end style dan bentuk kombinasi linearnya adalah begin mathsize 14px style 6 straight i with rightwards arrow on top minus 10 straight j with rightwards arrow on top end style.

1

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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