Roboguru

Jika dan sudut antara . Nilai adalah ....

Pertanyaan

Jika open vertical bar straight a close vertical bar equals 3 comma space open vertical bar straight b close vertical bar equals 10 dan sudut antara straight a with rightwards harpoon with barb upwards on top space dan space straight b with rightwards harpoon with barb upwards on top space adalah space 30 degree. Nilai straight a with rightwards harpoon with barb upwards on top. straight b with rightwards harpoon with barb upwards on top spaceadalah ....

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards harpoon with barb upwards on top. straight b with rightwards harpoon with barb upwards on top space end cell equals cell open vertical bar straight a with rightwards harpoon with barb upwards on top close vertical bar cross times open vertical bar straight b with rightwards harpoon with barb upwards on top close vertical bar cross times cos 30 degree end cell row blank equals cell 3 cross times 10 cross times 1 half square root of 3 end cell row blank equals cell 15 square root of 3 end cell end table

Jadi Nilai straight a with rightwards harpoon with barb upwards on top. straight b with rightwards harpoon with barb upwards on top space equals 15 square root of 3

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 07 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui koordinat titik , dan . Hasil perkalian  adalah ...

Pembahasan Soal:

Diketahui koordinat titik begin mathsize 14px style straight P open parentheses 3 comma space minus 1 comma space 4 close parentheses comma space straight Q open parentheses negative 2 comma space 1 comma space minus 5 close parentheses end style, dan begin mathsize 14px style straight R open parentheses 4 comma space 3 comma space minus 2 close parentheses end style, maka

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 straight Q minus straight P end cell row blank equals cell open parentheses table row cell negative 2 end cell row 1 row cell negative 5 end cell end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell row 2 row cell negative 9 end cell end table close parentheses end cell row blank blank blank row cell PR with rightwards arrow on top end cell equals cell straight R minus straight P end cell row blank equals cell open parentheses table row 4 row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 4 row cell negative 6 end cell end table close parentheses end cell end table end style 

Sehingga hasil perkalian dot productnya yaitu sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with rightwards arrow on top times PR with rightwards arrow on top end cell equals cell open parentheses table row cell negative 5 end cell row 2 row cell negative 9 end cell end table close parentheses times open parentheses table row 1 row 4 row cell negative 6 end cell end table close parentheses end cell row blank equals cell negative 5 plus 8 plus 54 end cell row blank equals 57 end table end style  

Jadi, tidak ada jawaban yang tepat. 

1

Roboguru

Diketahui vektor  . Nilai sinus sudut antara  adalah .....

Pembahasan Soal:

Ingat rumus perkalian titik pada vektor :

a with rightwards arrow on top. b with rightwards arrow on top equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar cos space A  open parentheses table row 3 row 4 row cell negative 5 end cell end table close parentheses. open parentheses table row 1 row cell negative 2 end cell row 2 end table close parentheses equals square root of 3 squared plus 4 squared plus left parenthesis negative 5 right parenthesis squared. end root square root of 1 squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root. cos space alpha  3 minus 8 minus 10 equals square root of 9 plus 16 plus 25 end root. square root of 1 plus 4 plus 4 end root. cos space alpha  minus 15 equals square root of 50. square root of 9. cos space alpha  minus 15 equals 5 square root of 2.3 space cos space alpha  cos space alpha equals negative fraction numerator 1 over denominator square root of 2 end fraction    sin space alpha equals square root of 1 minus cos squared alpha end root equals square root of 1 minus open parentheses negative fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared end root equals square root of 1 minus 1 half end root equals 1 half square root of 2    bold Catatan bold thin space bold colon  Karena space sudut space antara space dua space vektor space bernilai space 0 degree less or equal than straight alpha less or equal than 180 degree comma space maka  sin space straight alpha space tidaklah space negatif.

0

Roboguru

Diketahui  dan . Nilai dari  ...

Pembahasan Soal:

Misal terdapat vektor begin mathsize 14px style a with rightwards arrow on top equals a subscript 1 i with hat on top plus a subscript 2 j with hat on top plus a subscript 3 k with hat on top end style dan begin mathsize 14px style b with rightwards arrow on top equals b subscript 1 i with hat on top plus b subscript 2 j with hat on top plus b subscript 3 k with hat on top end style, berlaku rumus perkalian dot sebagai berikut.

begin mathsize 14px style 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 end style

Dari dua vektor yang diketahui di atas, dapat ditentukan hasil berikut.

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 cell open parentheses table row 7 row cell negative 1 end cell row 2 end table close parentheses open parentheses table row 1 row 2 row cell negative 12 end cell end table close parentheses end cell row blank equals cell 7 times 1 plus open parentheses negative 1 close parentheses times 2 plus 2 times open parentheses negative 12 close parentheses end cell row blank equals cell 7 minus 2 minus 24 end cell row blank equals cell negative 19 end cell end table end style

Dengan demikian, begin mathsize 14px style c with rightwards arrow on top times d with rightwards arrow on top equals negative 19 end style 

0

Roboguru

Diketahui vektor . Nilai sinus sudut antara vektor dan =....

Pembahasan Soal:

c o s space theta equals fraction numerator p ⃗. q with rightwards arrow on top over denominator vertical line p ⃗ vertical line. vertical line q ⃗ vertical line end fraction equals fraction numerator i plus j minus 4 k right parenthesis. left parenthesis negative 2 i minus j right parenthesis over denominator square root of 1 squared plus 1 squared plus left parenthesis negative 4 right parenthesis squared end root. square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus 0 squared end root end fraction  equals fraction numerator negative 2 minus 1 minus 0 over denominator square root of 18. square root of 5 end fraction equals fraction numerator negative 3 over denominator square root of 90 end fraction equals fraction numerator negative 3 over denominator 3 square root of 10 end fraction equals fraction numerator negative 1 over denominator square root of 10 end fraction equals negative 1 over 10 square root of 10  M a k a comma D e n g a n space i d e n t i t a s space s i n space theta equals  square root of left parenthesis 1 minus cos squared theta end root  equals square root of 1 minus open parentheses negative 1 over 10 square root of 10 right parenthesis squared close parentheses end root  equals 3 over 10 square root of 10

0

Roboguru

Diketahui , sudut antara  dan  adalah . Perkalian skalar antar dua vektor tersebut adalah ....

Pembahasan Soal:

Ingat kembali konsep perkalian skalar pada vektor sebagai berikut:

Jika vektor a with rightwards harpoon with barb upwards on top mempunyai panjang open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar, vektor b with rightwards harpoon with barb upwards on top mempunyai panjang open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar dan  alpha adalah sudut antara vektor a with rightwards harpoon with barb upwards on top dan b with rightwards harpoon with barb upwards on top, maka perkalian skalar vektor a with rightwards harpoon with barb upwards on top dan b with rightwards harpoon with barb upwards on top adalah

a with rightwards harpoon with barb upwards on top. b with rightwards harpoon with barb upwards on top equals open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar cos space alpha

Diketahui dari soal bahwa  open vertical bar p with rightwards harpoon with barb upwards on top close vertical bar equals 8 space dan space open vertical bar q with rightwards harpoon with barb upwards on top close vertical bar equals 10, sudut antara p dan q adalah alpha equals 60 degree, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards harpoon with barb upwards on top. q with rightwards harpoon with barb upwards on top end cell equals cell open vertical bar p with rightwards harpoon with barb upwards on top close vertical bar open vertical bar q with rightwards harpoon with barb upwards on top close vertical bar cos space alpha end cell row blank equals cell 8.10. cos space 60 degree end cell row blank equals cell 80.1 half end cell row blank equals 40 end table

Perkalian skalar vektor p with rightwards harpoon with barb upwards on top dan q with rightwards harpoon with barb upwards on top adalah 40.

Jadi, tidak ada pilihan jawaban yang tepat.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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