Jika vektor dan vektor , hasil kali adalah ….

Pertanyaan

Jika vektor $A with italic rightwards harpoon with barb upwards on top space equals space 2 straight i space plus space 3 straight j space plus space 4 straight k$ dan vektor $B with rightwards harpoon with barb upwards on top space equals space 3 straight i space plus space 5 straight k$ , hasil kali $A with rightwards harpoon with barb upwards on top cross times B with rightwards harpoon with barb upwards on top$ adalah ….

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... $undefined$

Pembahasan Video:

Pembahasan Soal:

$A with italic rightwards harpoon with barb upwards on top space equals space 2 straight i space plus space 3 straight j space plus space 4 straight k B with rightwards harpoon with barb upwards on top space equals space 3 straight i space plus space 5 straight k A with italic rightwards harpoon with barb upwards on top italic cross times B with italic rightwards harpoon with barb upwards on top equals open vertical bar table row straight i straight j straight k row 2 3 4 row 3 0 5 end table close vertical bar equals left parenthesis 3.5 minus 0.4 right parenthesis straight i plus left parenthesis 4.3 minus 2.5 right parenthesis straight j plus left parenthesis 2.0 minus 3.3 right parenthesis straight k A with italic rightwards harpoon with barb upwards on top italic space italic cross times B with italic rightwards harpoon with barb upwards on top equals 15 straight i plus 2 straight j minus 9 straight k$

Jadi, jawaban yang tepat adalah 15i+2j-9k

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 30 Agustus 2021

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Berapa resultan dari dua buah vektor yg berhimpit pangkalnya membentuk sudut yang besar vektornya 3 N dan 4 N?

Pembahasan Soal:

Diketahui:
$θ F_{1} F_{2} = = = 6 0^{\circ} 3 N 4 N$

Ditanya:
$F_{R} = ?$

Pembahasan:
Soal ini membahas tentang resultan vektor metode analistis. Resultan vektor bisa kita hitung menggunakan rumus. Rumus yang kita gunakan adalah sebagai berikut:

$begin mathsize 14px style F subscript R space equals space square root of F subscript italic 1 to the power of italic 2 space plus italic space F subscript italic 2 to the power of italic 2 space plus space 2 space. space F subscript italic 1 space. italic space F subscript italic 2 space. space c o s italic space theta end root F subscript R space equals space square root of 3 squared space plus space 4 squared space plus space 2 space. space 3 space. space 4 space. space c o s space 60 degree end root F subscript R space equals space square root of 9 space plus space 16 space plus space 24 space. space bevelled 1 half end root F subscript R space equals space square root of 25 space plus space 12 end root F subscript R space equals space square root of 37 space straight N end style$

Jadi, resultan vektor tersebut adalah $begin mathsize 14px style square root of 37 space straight N end style$ . $begin mathsize 14px style space space end style$

Roboguru

Perhatikan gambar berikut! Besar resultan kedua vektor (A+B) adalah ....

Pembahasan Soal:

Diketahui

A = 2i +4j

B=6i+2j

Ditanya

Resultan vektor A dan B

Jawab

A+B=8i+6j

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank blank row cell open vertical bar A plus B close vertical bar end cell equals cell square root of 8 squared plus 6 squared end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table$

Sehingga jawaban yang benar adalah A

Roboguru

adalah tiga buah vektor gaya yang menghasilkan resultan nol seperti pada gambar Jika maka berturut-turut adalah ….

Pembahasan Soal:

$Diketahui colon space straight F subscript 3 equals 100 space straight N straight theta subscript 3 equals 120 straight theta subscript 2 equals 90 straight theta subscript 1 equals 150 ditanya colon space straight F subscript 1 space dan space straight F subscript 2 ? jawab colon fraction numerator straight F subscript 2 over denominator sin space 90 end fraction equals fraction numerator straight F subscript 3 over denominator sin space 150 end fraction straight F subscript 2 over 1 equals fraction numerator 100 over denominator begin display style 1 half end style square root of 3 end fraction straight F subscript 2 equals fraction numerator 200 over denominator square root of 3 end fraction straight N fraction numerator straight F subscript 1 over denominator sin space 150 end fraction equals fraction numerator straight F subscript 2 over denominator sin space 90 end fraction fraction numerator straight F subscript 1 over denominator begin display style 1 half end style end fraction equals 200 square root of 3 straight F subscript 1 equals 100 square root of 3 space straight N$

Jadi, jawaban yang benar adalah B.

Roboguru

Vektor A panjangnya 10 bersudut 90 derajat. Vektor B panjangnya 10 bersudut 210 derajat. Vektor C=A+B. Vektor C berapa panjangnya dan sudutnya? Gambarlah sketsanya!

Pembahasan Soal:

Gambar dari resultan vektor C=A+B adalah

Antara A dan B membentuk sudut 120° sehingga besar resultannya
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row bold italic C bold equals cell bold italic A bold plus bold italic B end cell row blank bold equals cell square root of bold A to the power of bold 2 bold plus bold B to the power of bold 2 bold plus bold 2 bold A bold B bold cos bold space bold 120 bold degree end root end cell row blank equals cell square root of 10 squared plus 10 squared plus 2 cross times 10 cross times 10 cross times open parentheses negative 1 half close parentheses end root end cell row blank equals cell square root of 100 plus 100 minus 100 end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table end style$

Roboguru

Resultan ketiga gaya pada gambar di samping adalah ...

Pembahasan Soal:

$begin mathsize 14px style T i n j a u space s u m b u space x space colon sum straight F subscript straight x equals straight F subscript 1 minus F subscript 2 sin invisible function application 30 to the power of o minus F subscript 3 cos invisible function application 60 to the power of 0 sum straight F subscript straight x equals 20 minus 20 open parentheses 1 half close parentheses minus 24 open parentheses 1 half close parentheses sum straight F subscript straight x equals negative 2 straight space straight N Tinjau space sumbu space straight y space colon sum straight F subscript straight y equals straight F subscript 2 cos invisible function application 30 to the power of 0 minus straight F subscript 3 sin invisible function application 60 to the power of 0 sum straight F subscript straight y equals 20 open parentheses 1 half square root of 3 close parentheses minus 24 left parenthesis 1 half square root of 3 right parenthesis sum straight F subscript straight y equals negative 2 square root of 3 straight space straight N Jadi comma space resultan space ketiga space vektor space tersebut space adalah space colon straight F subscript straight R equals square root of open parentheses sum straight F subscript straight x close parentheses squared plus open parentheses sum straight F subscript straight y close parentheses squared end root straight F subscript straight R equals square root of open parentheses negative 2 close parentheses squared plus open parentheses negative 2 square root of 3 close parentheses squared end root straight F subscript straight R equals square root of 4 plus 12 end root straight F subscript straight R equals square root of 16 equals 4 straight space straight N straight space end style$

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