Roboguru

Diberikan vektor  dan . Tentukan: b.

Pertanyaan

Diberikan vektor begin mathsize 14px style straight u with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 7 end cell row 1 end table close parentheses end style dan begin mathsize 14px style v with rightwards harpoon with barb upwards on top equals open parentheses table row 9 row cell negative 3 end cell end table close parentheses end style. Tentukan:

b. begin mathsize 14px style negative 2 straight u with rightwards harpoon with barb upwards on top times straight v with rightwards harpoon with barb upwards on top end style

Pembahasan Soal:

Perkalian skala dengan vektor dan konsep perkalian titik (dot product):

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 straight u with rightwards harpoon with barb upwards on top end cell equals cell negative 2 open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 14 row cell negative 2 end cell end table close parentheses end cell end table end style 

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 straight u with rightwards harpoon with barb upwards on top times straight v with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 14 row cell negative 2 end cell end table close parentheses times open parentheses table row 9 row cell negative 3 end cell end table close parentheses end cell row blank equals cell 14 times 9 plus left parenthesis negative 2 right parenthesis left parenthesis negative 3 right parenthesis end cell row blank equals cell 126 plus 6 end cell row blank equals 132 end table end style 

Jadi, Error converting from MathML to accessible text..

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui  dan

Pembahasan Soal:

Diketahui a with rightwards harpoon with barb upwards on top equals 4 i plus j plus 5 k dan b with rightwards harpoon with barb upwards on top equals 2 i plus j minus 5 k 

a. Ingat kembali jika a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k dan b with rightwards harpoon with barb upwards on top equals b subscript 1 i plus b subscript 2 j plus b subscript 3 k maka a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals left parenthesis a subscript 1 plus b subscript 1 right parenthesis i plus left parenthesis a subscript 2 plus b subscript 2 right parenthesis j plus left parenthesis a subscript 3 plus b subscript 3 right parenthesis k 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 4 plus 2 right parenthesis i plus left parenthesis 1 plus 1 right parenthesis j plus left parenthesis 5 plus left parenthesis negative 5 right parenthesis right parenthesis k end cell row blank equals cell 6 i plus 2 j end cell end table 

Jadi, a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals 6 i plus 2 j.

b. Ingat kembali bahwa jika a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k dan b with rightwards harpoon with barb upwards on top equals b subscript 1 i plus b subscript 2 j plus b subscript 3 k maka a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals left parenthesis a subscript 1 minus b subscript 1 right parenthesis i plus left parenthesis a subscript 2 minus b subscript 2 right parenthesis j plus left parenthesis a subscript 3 minus b subscript 3 right parenthesis k 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 4 minus 2 right parenthesis i plus left parenthesis 1 minus 1 right parenthesis j plus left parenthesis 5 minus left parenthesis negative 5 right parenthesis k end cell row blank equals cell 2 i plus 10 k end cell end table 

Jadi, a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals 2 i plus 10 k.

c. Ingat kembali bahwa misalkan k adalah bilangan skalar dan a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k maka  k a with rightwards harpoon with barb upwards on top equals k a subscript 1 i plus k a subscript 2 k plus k a subscript 3 k 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 4 i plus j plus 5 k right parenthesis minus left parenthesis 2 left parenthesis 2 i plus j minus 5 k right parenthesis right parenthesis end cell row blank equals cell left parenthesis 4 i plus j plus 5 k right parenthesis minus left parenthesis 4 i plus 2 j minus 10 k right parenthesis end cell row blank equals cell left parenthesis 4 minus 4 right parenthesis i plus left parenthesis 1 minus 2 right parenthesis j plus left parenthesis 5 minus left parenthesis negative 10 right parenthesis right parenthesis k end cell row blank equals cell negative j plus 15 k end cell end table 

Jadi, a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top equals negative j plus 15 k.

d. Ingat kembali bahwa jika a with rightwards harpoon with barb upwards on top equals a subscript 1 i plus a subscript 2 j plus a subscript 3 k dan b with rightwards harpoon with barb upwards on top equals b subscript 1 i plus b subscript 2 j plus b subscript 3 k maka a with rightwards harpoon with barb upwards on top times b with rightwards harpoon with barb upwards on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top end cell equals cell 2 left parenthesis 4 comma space 1 comma space 5 right parenthesis times 3 left parenthesis 2 comma space 1 comma space minus 5 right parenthesis end cell row blank equals cell left parenthesis 8 comma space 2 comma space 10 right parenthesis times left parenthesis 6 comma space 3 comma space minus 15 right parenthesis end cell row blank equals cell 8 times 6 plus 2 times 3 plus 10 times negative 15 end cell row blank equals cell 48 plus 6 minus 150 end cell row blank equals cell 54 minus 150 end cell row blank equals cell negative 96 end cell end table 

Jadi, 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top equals negative 96.

Dengan demikian, hasil yang diperoleh adalah a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top equals 6 i plus 2 ja with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top equals 2 i plus 10 k dan 2 a with rightwards harpoon with barb upwards on top times 3 b with rightwards harpoon with barb upwards on top equals negative 96.

0

Roboguru

Diketahui , , dan .  dan  berturut-turut mewakili vektor  dan . Tentukan: d.

Pembahasan Soal:

Jika a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses, maka a with rightwards arrow on top times b with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses times open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses end cell row blank equals cell a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 end cell end table 

Vektor Posisi adalah vektor yang berpangkal di pusat koordinat open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik open parentheses x comma space y close parentheses.

Diketahui straight A open parentheses 2 comma space 6 comma space minus 5 close parentheses, straight B open parentheses negative 1 comma space 3 comma space 7 close parentheses, dan straight C open parentheses 4 comma space minus 1 comma space 8 close parentheses.

Nilai vektor posisi akan sama dengan koordinat titik ujungnya, maka tentukan AB with rightwards arrow on top dan BC with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 end cell row 3 row 7 end table close parentheses minus open parentheses table row 2 row 6 row cell negative 5 end cell end table close parentheses end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 minus 2 end cell row cell 3 minus 6 end cell row cell 7 plus 5 end cell end table close parentheses end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses end cell row cell BC with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus b with rightwards arrow on top end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row 4 row cell negative 1 end cell row 8 end table close parentheses minus open parentheses table row cell negative 1 end cell row 3 row 7 end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row cell 4 plus 1 end cell row cell negative 1 minus 3 end cell row cell 8 minus 7 end cell end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses end cell end table   

d. open parentheses 2 u with rightwards arrow on top minus 3 v with rightwards arrow on top close parentheses squared

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 u with rightwards arrow on top minus 3 v with rightwards arrow on top close parentheses squared end cell row blank equals cell 4 open parentheses u with rightwards arrow on top close parentheses squared minus 12 open parentheses u with rightwards arrow on top times v with rightwards arrow on top close parentheses plus 9 open parentheses v with rightwards arrow on top close parentheses squared end cell row blank equals cell 4 open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses squared minus 12 open parentheses open parentheses table row cell negative 3 end cell row cell negative 3 end cell row cell negative 3 end cell end table close parentheses times open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses close parentheses plus 9 open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses squared end cell row blank equals cell 4 open parentheses open parentheses negative 3 close parentheses squared plus open parentheses negative 3 close parentheses squared plus 12 squared close parentheses minus 12 open parentheses negative 15 plus 12 plus 12 close parentheses plus 9 open parentheses 5 squared plus open parentheses negative 4 close parentheses squared plus 1 squared close parentheses end cell row blank equals cell 4 times 162 minus 12 times 9 plus 9 times 42 end cell row blank equals cell 648 minus 108 plus 378 end cell row blank equals 918 end table end style 

Jadi, Error converting from MathML to accessible text..

0

Roboguru

Diberikan vektor . Jika vektor  tegak lurus vektor , maka hasil dari adalah ....

Pembahasan Soal:

Jika vektor begin mathsize 14px style a with rightwards arrow on top end style tegak lurus vektor begin mathsize 14px style b with rightwards arrow on top end style, maka begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top equals 0 end style 

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

Sehingga vektor begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses end style

Menentukan hasil dari begin mathsize 14px style open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end cell equals cell open parentheses open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses minus open parentheses table row 4 row cell negative 3 end cell row 6 end table close parentheses close parentheses times open parentheses 2 open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 5 row cell negative 7 end cell end table close parentheses times open parentheses table row 4 row cell negative 2 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses 4 close parentheses plus 5 open parentheses negative 2 close parentheses plus open parentheses negative 7 close parentheses open parentheses 6 close parentheses end cell row blank equals cell negative 4 plus open parentheses negative 10 close parentheses plus open parentheses negative 42 close parentheses end cell row blank equals cell negative 56 end cell end table end style 

Jadi, hasil dari begin mathsize 14px style open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end style adalah begin mathsize 14px style negative 56 end style.

0

Roboguru

Diketahui:  dan  Tentukan: 5)

Pembahasan Soal:

Gunakan konsep perkalian dua vektor dan operasi dot product pada dua vektor dengan a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell row cell a subscript 3 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell row cell b subscript 3 end cell end table close parentheses.

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3

AKan ditentukan hasil dari 3 open parentheses a with rightwards arrow on top times b with rightwards arrow on top close parentheses.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell 3 open parentheses a with rightwards arrow on top times b with rightwards arrow on top close parentheses end cell equals cell 3 open square brackets 4 times 8 plus open parentheses negative 2 close parentheses times 0 plus 4 times open parentheses negative 6 close parentheses close square brackets end cell row blank equals cell 3 open parentheses 32 plus 0 minus 24 close parentheses end cell row blank equals cell 3 open parentheses 8 close parentheses end cell row blank equals 24 end table

Jadi, diperoleh 3 open parentheses a with rightwards arrow on top times b with rightwards arrow on top close parentheses equals 24.

0

Roboguru

Diketahui vektor  dan . Jika hasil , tentukan: a. nilai   b. hasil

Pembahasan Soal:

Nilai size 14px a adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top times v with rightwards arrow on top end cell equals cell negative 6 end cell row cell open parentheses table row cell negative 5 end cell row 7 end table close parentheses times open parentheses table row 4 row a end table close parentheses end cell equals cell negative 6 end cell row cell open parentheses negative 5 close parentheses times 4 plus 7 a end cell equals cell negative 6 end cell row cell negative 20 plus 7 a end cell equals cell negative 6 end cell row cell 7 a end cell equals cell negative 6 plus 20 end cell row a equals cell 14 over 7 end cell row a equals 2 end table end style 

Sehingga, hasil begin mathsize 14px style open parentheses 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top close parentheses times open parentheses u with rightwards arrow on top minus 2 v with rightwards arrow on top close parentheses end style adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top right parenthesis times left parenthesis u with rightwards arrow on top minus 2 v with rightwards arrow on top right parenthesis end cell equals cell open parentheses 2 open parentheses table row cell negative 5 end cell row 7 end table close parentheses plus 3 open parentheses table row 4 row 2 end table close parentheses close parentheses times open parentheses open parentheses table row cell negative 5 end cell row 7 end table close parentheses minus 2 open parentheses table row 4 row 2 end table close parentheses close parentheses end cell row blank equals cell open parentheses open parentheses table row cell negative 10 end cell row 14 end table close parentheses plus open parentheses table row 12 row 6 end table close parentheses close parentheses times open parentheses open parentheses table row cell negative 5 end cell row 7 end table close parentheses minus open parentheses table row 8 row 4 end table close parentheses close parentheses end cell row blank equals cell open parentheses table row 2 row 20 end table close parentheses times open parentheses table row cell negative 13 end cell row 3 end table close parentheses end cell row blank equals cell 2 times open parentheses negative 13 close parentheses plus 20 times 3 end cell row blank equals cell negative 26 plus 60 end cell row blank equals 34 end table end style 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top right parenthesis times left parenthesis u with rightwards arrow on top minus 2 v with rightwards arrow on top right parenthesis 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 34 end table 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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