Tiga buah vektor sebagai berikut: = 3i + 5j + 2k = 5i – 3k = 6j + 2k Hasil dari adalah ….

Pertanyaan

Tiga buah vektor sebagai berikut:
$L with rightwards harpoon with barb upwards on top$ = 3i + 5j + 2k
$M with rightwards harpoon with barb upwards on top$ = 5i – 3k
$N with rightwards harpoon with barb upwards on top$ = 6j + 2k
Hasil dari $L with rightwards harpoon with barb upwards on top minus 2 M with rightwards harpoon with barb upwards on top plus 3 N with rightwards harpoon with barb upwards on top$ adalah ….

7i + 23j + 14k
7i + 23j - 14k
-7i + 23j + 14k
-7i - 23j + 14k
7i - 23j - 14k

Pembahasan Video:

Pembahasan Soal:

Dit : $L with rightwards harpoon with barb upwards on top minus 2 M with rightwards harpoon with barb upwards on top plus 3 N with rightwards harpoon with barb upwards on top$ ?

Dik:

$L with rightwards harpoon with barb upwards on top$ = 3i + 5j + 2k
$M with rightwards harpoon with barb upwards on top$ = 5i – 3k
$N with rightwards harpoon with barb upwards on top$ = 6j + 2k

menggunakan konsep pengurangan dan pertambahan dalam vektor :

$equals left parenthesis 3 straight i space plus space 5 straight j space plus space 2 straight k space right parenthesis minus 2 left parenthesis 5 straight i space – space 3 straight k right parenthesis plus 3 left parenthesis space 6 straight j space plus space 2 straight k right parenthesis equals negative 7 straight i plus 23 straight j plus 14 straight k$

Jadi, jawaban yang tepat adalah C

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 30 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Vektor gaya , , dan terletak pada sebuah diagram kartesius seperti gambar : Resultan ketiga vektor adalah ...

Pembahasan Soal:

Diketahui :

$straight F subscript 1 equals 12 space straight N straight F subscript 2 equals 10 space straight N straight F subscript 3 equals 8 space straight N θF subscript 1 equals 30 degree θF subscript 3 equals 90 degree minus 60 degree equals 30 degree straight F subscript straight R ?$

Tinjau sumbu x :

$sum straight F subscript straight x equals straight F subscript 1 space cos space 30 degree space minus space straight F subscript 3 space cos space 30 degree sum straight F subscript straight x equals 12 space open parentheses 1 half square root of 3 close parentheses space minus space 8 open parentheses 1 half square root of 3 close parentheses sum straight F subscript straight x equals 6 square root of 3 minus 4 square root of 3 sum straight F subscript straight x equals 2 square root of 3 space straight N$

Tinjau sumbu y :

$sum straight F subscript straight y equals straight F subscript 1 space sin space 30 degree space minus space straight F subscript 3 space sin space 30 degree minus space straight F subscript 2 sum straight F subscript straight y equals 12 space open parentheses 1 half close parentheses space minus space 8 open parentheses 1 half close parentheses minus 10 sum straight F subscript straight y equals 6 minus 4 minus 10 sum straight F subscript straight y equals negative 8 space straight N$

Maka, besarnya resultan gaya dengan menggunakan vektor adalah :

$straight F subscript straight R equals square root of open parentheses sum straight F subscript straight x close parentheses squared plus space open parentheses sum straight F subscript straight y close parentheses squared end root straight F subscript straight R equals square root of open parentheses 2 square root of 3 close parentheses squared plus space open parentheses negative 8 close parentheses squared end root straight F subscript straight R equals square root of 76 space straight N$

Roboguru

Perhatikan gambar vektor dibawah ini! Jika besar vektor adalah 24 N dan besar vektor adalah 10 N, besar resultan kedua vektor tersebut adalah ....

Pembahasan Soal:

Uraikan vektor-vektor tersebut dalam arah vertikal dan horizontal seperti berikut ini.

Jumlah komponen vektor dalam arah horizontal (sumbu x) adalah:

$begin mathsize 14px style sum for space of begin inline style F subscript x end style equals F subscript 2 space sin space 37 to the power of straight o begin inline style sum for space of end style begin inline style F subscript x end style begin inline style equals end style begin inline style 10 end style begin inline style open parentheses begin display style 0 comma 6 end style close parentheses end style begin inline style sum for space of end style begin inline style F subscript x end style begin inline style equals end style 6 space begin inline style straight N end style end style$

Jumlah komponen vektor dalam arah vertikal (sumbu y) adalah:

$begin mathsize 14px style sum for space of F subscript y equals F subscript 1 space minus F subscript 2 space cos space 37 to the power of straight o begin inline style sum for space of end style begin inline style F subscript y end style begin inline style equals end style 24 minus 10 left parenthesis 0 comma 8 right parenthesis begin inline style sum for space of end style begin inline style F subscript y end style begin inline style equals end style 24 minus 8 begin inline style sum for space of end style begin inline style F subscript y end style begin inline style equals end style 16 space begin inline style straight N end style end style$

Maka besar resultan kedua vektor dapat dicari dengan penguraian vektor.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line R with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis sum open vertical bar stack F subscript x with rightwards arrow on top close vertical bar right parenthesis squared plus left parenthesis sum open vertical bar stack F subscript y with rightwards arrow on top close vertical bar right parenthesis squared end root end cell row cell vertical line R with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis 6 right parenthesis squared plus left parenthesis 16 right parenthesis squared end root end cell row cell vertical line R with rightwards arrow on top vertical line end cell equals cell square root of 292 end cell row cell vertical line R with rightwards arrow on top vertical line end cell equals cell 2 square root of 73 blank straight N end cell end table end style$

Jadi, jawaban yang tepat adalah A.

Roboguru

Jika besarnya resultan dan selisih kedua vektor sama, maka besarnya sudut apit kedua vektor adalah ….

Pembahasan Soal:

Diketahui: Resultan vektor = Selisih vektor

Ditanya: sudut apit (θ) = ...?

Jawaban:

Resultan vektor dirumuskan sebagai:

$R equals square root of open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end root$

Sedangkan selisih vektor dirumuskan sebagai:

$S equals square root of open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end root$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row R equals S row cell square root of open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end root end cell equals cell square root of open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos italic space theta end root end cell row cell open parentheses square root of open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end root close parentheses squared end cell equals cell open parentheses square root of open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end root close parentheses squared end cell row cell open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end cell equals cell open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end cell row cell 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta plus 2 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos space theta end cell equals 0 row cell 4 open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar space cos italic space theta end cell equals 0 row cell cos space theta end cell equals 0 row theta equals cell cos to the power of negative 1 end exponent open parentheses 0 close parentheses end cell row theta equals cell 90 degree end cell end table$

Dengan demikian, besar sudut apit kedua vektor adalah 90°.

Jadi, tidak ada jawaban yang tepat.

Roboguru

Dua buah gaya yang sama besar 10 N membentuk sudut 120° satu sama lain. Selisih kedua vektor tersebut adalah ...

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style F subscript 1 equals F subscript 2 equals 10 space N alpha equals 120 to the power of 0 end style$

Ditanya: $begin mathsize 14px style S end style$ ?

Resultan gaya adalah hasil operasi hitung antara dua vektor gaya atau lebih

Penyelesaian:

$S equals F subscript 1 minus F subscript 2 S equals square root of F subscript 1 squared plus F subscript 2 squared minus 2 F subscript 1 F subscript 2 cos alpha end root S equals square root of 10 squared plus 10 squared minus 2.10.10 cos left parenthesis 120 right parenthesis end root S equals square root of 200 minus 200 left parenthesis negative bevelled 1 half right parenthesis end root S equals square root of 300 S equals 10 square root of 3 space end root straight N$

Jadi, selisih kedua vektor tersebut adalah $begin mathsize 14px style 10 square root of 3 space straight N end style$ . (D) $undefined$

Roboguru

Vektor , , dan diletakkan pada diagram Cartesius seperti pada gambar. Berapa resultan ketiga vektor tersebut?

Pembahasan Soal:

$Error converting from MathML to accessible text.$

Hitung total gaya di sumbu - x:

$Error converting from MathML to accessible text.$

Hitung total gaya di sumbu - y:

$Error converting from MathML to accessible text.$

Maka total gayanya adalah :

$begin mathsize 14px style begin inline style straight F subscript straight R equals square root of left parenthesis straight capital sigma space straight F subscript straight x right parenthesis squared plus left parenthesis straight capital sigma space straight F subscript straight y right parenthesis squared end root straight F subscript straight R equals square root of left parenthesis 8 right parenthesis squared plus left parenthesis 6 right parenthesis squared end root straight F subscript straight R equals square root of 100 straight F subscript straight R equals 10 space straight N end style end style$

Roboguru