Roboguru

Diketahui ,  dan . Jika . Hitunglah .

Pertanyaan

Diketahui begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals 3 straight i minus 2 straight j end styleError converting from MathML to accessible text. dan Error converting from MathML to accessible text.. Jika Error converting from MathML to accessible text.. Hitunglah begin mathsize 14px style straight m plus straight n end style.

Pembahasan Soal:

Konsep Perkalian skala dengan vektor dan kesamaan 2 vektor:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight r with rightwards harpoon with barb upwards on top end cell equals cell straight m straight a with rightwards harpoon with barb upwards on top plus straight n straight b with rightwards harpoon with barb upwards on top end cell row cell 7 straight i minus 8 straight j end cell equals cell straight m left parenthesis 3 straight i minus 2 straight j right parenthesis plus straight n left parenthesis negative straight i plus 4 straight j right parenthesis end cell row cell open parentheses table row 7 row cell negative 8 end cell end table close parentheses end cell equals cell straight m open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus straight n open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row cell open parentheses table row 7 row cell negative 8 end cell end table close parentheses end cell equals cell open parentheses table row cell 3 straight m end cell row cell negative 2 straight m end cell end table close parentheses plus open parentheses table row cell negative straight n end cell row cell 4 straight n end cell end table close parentheses end cell row cell open parentheses table row 7 row cell negative 8 end cell end table close parentheses end cell equals cell open parentheses table row cell 3 straight m minus straight n end cell row cell negative 2 straight m plus 4 straight n end cell end table close parentheses end cell end table end style 

Dari kesamaan 2 vektor diperoleh:

Persamaan begin mathsize 14px style 3 straight m minus straight n equals 7 end style dan Error converting from MathML to accessible text. .

Dengan metode eliminasi - substitusi:

begin mathsize 14px style table row cell 3 straight m minus straight n equals 7 rightwards arrow end cell cell 12 straight m minus 4 straight n equals 28 end cell row cell negative 2 straight m plus 4 straight n equals negative 8 rightwards arrow end cell cell negative 2 straight m plus 4 straight n equals negative 8 space plus end cell row blank cell 10 space straight m equals 20 end cell row blank cell straight m equals 2 end cell row blank cell 3 straight m minus straight n equals 7 end cell row blank cell 3 times 2 minus straight n equals 7 end cell row blank cell 6 minus straight n equals 7 end cell row blank cell straight n equals negative 1 end cell end table end style 

Jadi, begin mathsize 14px style straight m plus straight n equals 2 minus 1 equals 1 end style.

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 . Tentukan vektor-vektor berikut. e.

Pembahasan Soal:

Gunakan konsep pekalian skalar dengan vektor dan penjumlahan dua vektor sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell k m with rightwards arrow on top end cell equals cell k open parentheses table row e row f end table close parentheses equals open parentheses table row cell k times e end cell row cell k times f end cell end table close parentheses end cell row cell m with rightwards arrow on top plus n with rightwards arrow on top end cell equals cell open parentheses table row e row f end table close parentheses plus open parentheses table row g row h end table close parentheses equals open parentheses table row cell e plus g end cell row cell f plus h end cell end table close parentheses end cell end table end style  

Perhatikan perhitungan sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus 4 open parentheses table row 6 row 4 end table close parentheses plus open parentheses table row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row cell 4 cross times 6 end cell row cell 4 cross times 4 end cell end table close parentheses plus open parentheses table row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row 24 row 16 end table close parentheses plus open parentheses table row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 plus 24 plus 2 end cell row cell 5 plus 16 plus open parentheses negative 3 close parentheses end cell end table close parentheses end cell row cell b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a with rightwards arrow on top end cell equals cell open parentheses table row 23 row 18 end table close parentheses end cell end table end style   

Jadi, diperoleh begin mathsize 14px style b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a with rightwards arrow on top equals open parentheses table row 23 row 18 end table close parentheses end style.

0

Roboguru

Diketahui vektor  dan . Jika , hasil  adalah ...

Pembahasan Soal:

Dengan menggunakan konsep perkalian skalar dengan vektor dan penjumlahanan pada vektor dalam ruang dimensi tiga maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight w with rightwards arrow on top end cell equals cell 3 straight u with rightwards arrow on top plus 5 straight v with rightwards arrow on top end cell row blank equals cell 3 open parentheses table row 2 row 5 row cell negative 8 end cell end table close parentheses plus 5 open parentheses table row 0 row cell negative 3 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row 6 row 15 row cell negative 24 end cell end table close parentheses plus open parentheses table row 0 row cell negative 15 end cell row 20 end table close parentheses end cell row blank equals cell open parentheses table row cell 6 plus 0 end cell row cell 15 plus open parentheses negative 15 close parentheses end cell row cell negative 24 plus 20 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row 0 row cell negative 4 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 straight u with rightwards arrow on top minus 3 straight v with rightwards arrow on top minus 2 straight w with rightwards arrow on top end cell equals cell open parentheses table row 2 row 5 row cell negative 8 end cell end table close parentheses minus 3 open parentheses table row 0 row cell negative 3 end cell row 4 end table close parentheses minus 2 open parentheses table row 6 row 0 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row 5 row cell negative 8 end cell end table close parentheses minus open parentheses table row 0 row cell negative 9 end cell row 12 end table close parentheses minus open parentheses table row 12 row 0 row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 minus 0 minus 12 end cell row cell 5 minus open parentheses negative 9 close parentheses minus 0 end cell row cell negative 8 minus 12 minus open parentheses negative 8 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 10 end cell row 14 row cell negative 12 end cell end table close parentheses end cell end table end style 

Dengan demikian, hasil dari begin mathsize 14px style straight u with rightwards arrow on top minus 3 straight v with rightwards arrow on top minus 2 straight w with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row cell negative 10 end cell row 14 row cell negative 12 end cell end table close parentheses end style

0

Roboguru

Jika ,  dan  tentukan

Pembahasan Soal:

Diketahui:

Vektor begin mathsize 14px style a with rightwards arrow on top equals open square brackets table row 1 row cell negative 1 end cell end table close square brackets end stylebegin mathsize 14px style b with rightwards arrow on top equals open square brackets table row 4 row cell negative 2 end cell end table close square brackets end style dan begin mathsize 14px style c with rightwards arrow on top equals open square brackets table row cell negative 3 end cell row 3 end table close square brackets end style 

Tentukan vektor begin mathsize 14px style d with rightwards arrow on top equals a with rightwards arrow on top plus 3 b with rightwards arrow on top minus 2 c with rightwards arrow on top end style, sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell d with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus 3 b with rightwards arrow on top minus 2 c with rightwards arrow on top end cell row blank equals cell open square brackets table row 1 row cell negative 1 end cell end table close square brackets plus 3 open square brackets table row 4 row cell negative 2 end cell end table close square brackets minus 2 open square brackets table row cell negative 3 end cell row 3 end table close square brackets end cell row blank equals cell open square brackets table row 1 row cell negative 1 end cell end table close square brackets plus open square brackets table row 12 row cell negative 6 end cell end table close square brackets minus open square brackets table row cell negative 6 end cell row 6 end table close square brackets end cell row blank equals cell open square brackets table row cell 1 plus 12 minus open parentheses negative 6 close parentheses end cell row cell negative 1 plus open parentheses negative 6 close parentheses minus 6 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 1 plus 12 plus 6 end cell row cell negative 1 minus 6 minus 6 end cell end table close square brackets end cell row blank equals cell open square brackets table row 19 row cell negative 13 end cell end table close square brackets end cell end table end style

Maka, begin mathsize 14px style d with rightwards arrow on top equals open square brackets table row 19 row cell negative 13 end cell end table close square brackets end style.

0

Roboguru

Diketahui , , dan . Tentukan vektor-vektor berikut. f.

Pembahasan Soal:

Gunakan konsep pekalian skalar dengan vektor dan penjumlahan dua vektor sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell k m with rightwards arrow on top end cell equals cell k open parentheses table row e row f end table close parentheses equals open parentheses table row cell k times e end cell row cell k times f end cell end table close parentheses end cell row cell m with rightwards arrow on top plus n with rightwards arrow on top end cell equals cell open parentheses table row e row f end table close parentheses plus open parentheses table row g row h end table close parentheses equals open parentheses table row cell e plus g end cell row cell f plus h end cell end table close parentheses end cell end table end style  

Perhatikan perhitungan sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell 10 open parentheses table row 2 row cell negative 3 end cell end table close parentheses plus 4 open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row 6 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 10 cross times 2 end cell row cell 10 cross times open parentheses negative 3 close parentheses end cell end table close parentheses plus open parentheses table row cell 4 cross times open parentheses negative 3 close parentheses end cell row cell 4 cross times 5 end cell end table close parentheses plus open parentheses table row 6 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 20 row cell negative 30 end cell end table close parentheses plus open parentheses table row cell negative 12 end cell row 20 end table close parentheses plus open parentheses table row 6 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 20 plus open parentheses negative 12 close parentheses plus 6 end cell row cell negative 30 plus 20 plus 4 end cell end table close parentheses end cell row cell 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell open parentheses table row 14 row cell negative 6 end cell end table close parentheses end cell end table end style   

Jadi, diperoleh begin mathsize 14px style 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top equals open parentheses table row 14 row cell negative 6 end cell end table close parentheses end style.

0

Roboguru

Diketahui vektor  carilah vektor  sehingga memenuhi persamaan

Pembahasan Soal:

Diketahui vektor begin mathsize 14px style d with bar on top equals open parentheses table row 2 row 1 end table close parentheses comma space e with bar on top equals open parentheses table row cell negative 4 end cell row 2 end table close parentheses comma space f with bar on top equals open parentheses table row 0 row 5 end table close parentheses end style.

Dapat ditentukan persamaan berikut. 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 4 d with bar on top minus 2 x with bar on top end cell equals cell e with bar on top plus 3 f with bar on top end cell row cell negative 2 x with bar on top end cell equals cell e with bar on top plus 3 f with bar on top plus 4 d with bar on top end cell row cell negative 2 x with bar on top end cell equals cell open parentheses table row cell negative 4 end cell row 2 end table close parentheses plus 3 open parentheses table row 0 row 5 end table close parentheses plus 4 open parentheses table row 2 row 1 end table close parentheses end cell row cell negative 2 x with bar on top end cell equals cell open parentheses table row cell negative 4 end cell row 2 end table close parentheses plus open parentheses table row 0 row 15 end table close parentheses plus open parentheses table row 8 row 4 end table close parentheses end cell row cell negative 2 x with bar on top end cell equals cell open parentheses table row 4 row 21 end table close parentheses end cell row cell x with bar on top end cell equals cell open parentheses table row cell negative 2 end cell row cell negative 21 over 2 end cell end table close parentheses end cell end table end style

Dengan demikian, vektor begin mathsize 14px style x with bar on top equals open parentheses table row cell negative 2 end cell row cell negative 21 over 2 end cell end table close parentheses 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?

Membantu

Kurang Membantu

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