Roboguru

DIketahui  dan . Jika , tentukan hasil dari !

Pertanyaan

DIketahui begin mathsize 14px style vertical line p with rightwards arrow on top vertical line equals 5 end style dan size 14px vertical line size 14px q with size 14px rightwards arrow on top size 14px vertical line size 14px equals size 14px 6. Jika begin mathsize 14px style angle left parenthesis p comma space q right parenthesis equals 30 degree end style, tentukan hasil dari begin mathsize 14px style p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses end style!  space undefined 

Pembahasan Soal:

Dengan menggunakan rumus perkalian skalar antara dua vektor:

begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top equals vertical line a with rightwards arrow on top vertical line vertical line b with rightwards arrow on top vertical line cos space alpha end style    

Diperoleh

begin mathsize 14px style p with rightwards arrow on top times q with rightwards arrow on top equals vertical line p with rightwards arrow on top vertical line vertical line q with rightwards arrow on top vertical line cos space 30 degree p with rightwards arrow on top times q with rightwards arrow on top equals 5 cross times 6 cross times 1 half square root of 3 p with rightwards arrow on top times q with rightwards arrow on top equals 15 square root of 3 end style 

Nilai begin mathsize 14px style p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses end style

begin mathsize 14px style p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses equals p with rightwards arrow on top times p with rightwards arrow on top plus p with rightwards arrow on top times q with rightwards arrow on top p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses equals vertical line p with rightwards arrow on top vertical line squared plus 15 square root of 3 p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses equals 5 squared plus 15 square root of 3 p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses equals 25 plus 15 square root of 3 end style 

Jadi, nilai begin mathsize 14px style p with rightwards arrow on top times open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses end style adalah begin mathsize 14px style 25 plus 15 square root of 3 end style       undefined 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Alfi

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 29 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

DIketahui  dan . Jika , tentukan hasil dari !

Pembahasan Soal:

Dengan menggunakan rumus perkalian skalar antara dua vektor:

begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top equals vertical line a with rightwards arrow on top vertical line vertical line b with rightwards arrow on top vertical line cos space alpha end style    

Diperoleh

begin mathsize 14px style p with rightwards arrow on top times q with rightwards arrow on top equals vertical line p with rightwards arrow on top vertical line vertical line q with rightwards arrow on top vertical line cos space 30 degree p with rightwards arrow on top times q with rightwards arrow on top equals 5 cross times 6 cross times 1 half square root of 3 p with rightwards arrow on top times q with rightwards arrow on top equals 15 square root of 3 end style 

Nilai begin mathsize 14px style p with rightwards arrow on top times open parentheses p with rightwards arrow on top minus q with rightwards arrow on top close parentheses end style

begin mathsize 14px style p with rightwards arrow on top times left parenthesis p with rightwards arrow on top plus q with rightwards arrow on top right parenthesis equals p with rightwards arrow on top times p with rightwards arrow on top minus p with rightwards arrow on top times q with rightwards arrow on top p with rightwards arrow on top times left parenthesis p with rightwards arrow on top plus q with rightwards arrow on top right parenthesis equals vertical line p with rightwards arrow on top vertical line squared minus 15 square root of 3 p with rightwards arrow on top times left parenthesis p with rightwards arrow on top plus q with rightwards arrow on top right parenthesis equals 5 squared minus 15 square root of 3 p with rightwards arrow on top times left parenthesis p with rightwards arrow on top plus q with rightwards arrow on top right parenthesis equals 25 minus 15 square root of 3 end style  

Jadi, nilai begin mathsize 14px style p with rightwards arrow on top times open parentheses p with rightwards arrow on top minus q with rightwards arrow on top close parentheses end style adalah size 14px 25 size 14px minus size 14px 15 square root of size 14px 3        undefined 

0

Roboguru

Diketahui vektor  dan  sudut antara  adalah . Nilai dari ....

Pembahasan Soal:

Vektor  begin mathsize 14px style p with rightwards arrow on top equals open parentheses table row 1 row 2 end table close parentheses end style dan begin mathsize 14px style q with rightwards arrow on top equals open parentheses table row 4 row 2 end table close parentheses end style

 ingat rumus dot product pada vektor begin mathsize 14px style straight u times straight v equals vertical line straight u vertical line vertical line straight v vertical line cross times cosθ end style,maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top times q with rightwards arrow on top end cell equals cell vertical line p with rightwards arrow on top vertical line vertical line q with rightwards arrow on top vertical line cos beta end cell row cell open parentheses table row 1 row 2 end table close parentheses times open parentheses table row 4 row 2 end table close parentheses end cell equals cell square root of 1 squared plus 2 squared end root square root of 4 squared plus 2 squared end root cos beta end cell row cell 4 plus 4 end cell equals cell square root of 5 square root of 20 cos beta end cell row 8 equals cell square root of 25 cos beta end cell row 8 equals cell 5 cos beta end cell row cell cos beta end cell equals cell 8 over 5 end cell end table end style

Nilai dari begin mathsize 14px style cos beta equals end stylebegin mathsize 14px style 8 over 5 end style.

0

Roboguru

Vektor-vektor  dalam bentuk komponen masing-masing . Nilai m supaya kedua vektor tersebut saling tegak lurus adalah ....

Pembahasan Soal:

 Vektor begin mathsize 14px style c with rightwards arrow on top equals open parentheses table row 2 row m row cell 4 n end cell end table close parentheses semicolon d with rightwards arrow on top equals open parentheses table row cell 4 n end cell row cell negative 2 end cell row cell negative 2 end cell end table close parentheses end style

Vektor dikatakan tegak lurus apabila titik temu dua vektor tersebut membentuk sudut siku-siku dengan begin mathsize 14px style theta equals 90 degree end style. ingat rumus dot product pada vektor.

begin mathsize 14px style c with rightwards arrow on top times d with rightwards arrow on top equals vertical line c with rightwards arrow on top vertical line vertical line d with rightwards arrow on top vertical line cosθ end style

Karena nilai begin mathsize 14px style cos 90 degree equals 0 rightwards arrow c with rightwards arrow on top times d with rightwards arrow on top equals 0 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top times d with rightwards arrow on top end cell equals 0 row cell open parentheses table row 2 row m row cell 4 n end cell end table close parentheses open parentheses table row cell 4 n end cell row cell negative 2 end cell row cell negative 2 end cell end table close parentheses end cell equals 0 row cell 8 n plus negative 2 m minus 8 n end cell equals 0 row cell negative 2 m end cell equals 0 row blank rightwards arrow cell m equals 0 end cell end table end style

Jadi, Nilai m adalah 0.

0

Roboguru

Diketahui  , , dan . Jika vektor  tegak lurus terhadap vektor , vektor  adalah ....

Pembahasan Soal:

Vektor begin mathsize 14px style a equals open parentheses table row 4 row 2 row cell negative 5 end cell end table close parentheses end style, dan vektor begin mathsize 14px style b equals open parentheses table row 1 row 3 row x end table close parentheses end style

Vektor dikatakan tegak lurus apabila titik temu dua vektor tersebut membentuk sudut siku-siku dengan begin mathsize 14px style theta equals 90 degree end style. ingat rumus dot product pada vektor.

begin mathsize 14px style straight u times straight v equals vertical line straight u vertical line vertical line straight v vertical line cross times cosθ end style

Karena nilai begin mathsize 14px style cos 90 degree equals 0 rightwards arrow straight u times straight v equals 0 end style, maka

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

Vektor begin mathsize 14px style 2 a plus 3 b minus c end style yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a plus 3 b minus c end cell equals cell 2 open parentheses table row 4 row 2 row cell negative 5 end cell end table close parentheses plus 3 open parentheses table row 1 row 3 row 2 end table close parentheses minus open parentheses table row 6 row 5 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 8 row 4 row cell negative 10 end cell end table close parentheses plus open parentheses table row 3 row 9 row 6 end table close parentheses minus open parentheses table row 6 row 5 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 5 row 8 row cell negative 2 end cell end table close parentheses end cell end table end style

Jadi, vektor begin mathsize 14px style 2 a plus 3 b minus c end style adalah begin mathsize 14px style open parentheses table row 5 row 8 row cell negative 2 end cell end table close parentheses equals 5 top enclose i plus 8 top enclose j minus 2 top enclose k end style.

0

Roboguru

Diketahui: . Jika  adalah sudut antara  serta , maka nilai konstanta positif k adalah ....

Pembahasan Soal:

Nilai tan sama dengan 1 terjadi saat sudut alpha sebesar 45 derajat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan alpha end cell equals 1 row cell tan alpha end cell equals cell tan 45 degree end cell row blank rightwards arrow cell alpha equals 45 degree end cell end table end style

Vektor  begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 2 row k end table close parentheses space dan space c with rightwards arrow on top equals open parentheses table row 6 row 10 end table close parentheses end style

 ingat rumus dot product pada vektor begin mathsize 14px style straight a times c equals vertical line a vertical line vertical line c vertical line cross times cos alpha end style,maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times c with rightwards arrow on top end cell equals cell vertical line a with rightwards arrow on top vertical line vertical line c with rightwards arrow on top vertical line cos 45 degree end cell row cell open parentheses table row 2 row k end table close parentheses times open parentheses table row 6 row 10 end table close parentheses end cell equals cell square root of 2 squared plus k squared end root square root of 6 squared plus 10 squared end root cross times 1 half square root of 2 end cell row cell 12 plus 10 k end cell equals cell square root of 4 plus k squared end root square root of 136 cross times square root of 1 half end root end cell row blank equals cell square root of 4 plus k squared end root square root of 68 end cell row blank equals cell square root of 272 plus 68 k squared end root end cell row cell 144 plus 240 k plus 100 k squared end cell equals cell 272 plus 68 k squared end cell row cell 32 k squared plus 240 k minus 128 end cell equals 0 row cell 2 k squared plus 15 k minus 8 end cell equals 0 row cell left parenthesis 2 k minus 1 right parenthesis left parenthesis k plus 8 right parenthesis end cell equals 0 row blank rightwards arrow cell k equals negative 8 space logical or k equals 1 half end cell end table end style

Jadi, nilai konstanta positif begin mathsize 14px style k equals 1 half 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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