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Diketahui 3 buah vektor yaitu: a b c ​ = = = ​ − 8 i + 4 j ​ 3 i + 8 j ​ 4 i − y j ​ ​ Jika a ⋅ b = ∣ ∣ ​ c ∣ ∣ ​ , maka tentukan nilai y .

Diketahui 3 buah vektor yaitu:

Jika , maka tentukan nilai .space 

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

dan .

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table.

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Pembahasan

Jika dan , maka adalah: adalah panjang vektor , dengan: Diketahui: Jika , maka tentukan nilai . Jadi, dan .

Jika a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses, maka a with rightwards arrow on top times b with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses times open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses end cell row blank equals cell a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 end cell end table 

open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar adalah panjang vektor a with rightwards arrow on top, dengan:

open vertical bar a with rightwards arrow on top close vertical bar equals square root of open parentheses a subscript 1 close parentheses squared plus open parentheses a subscript 2 close parentheses squared end root 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell negative 8 i with rightwards arrow on top plus 4 j with rightwards arrow on top end cell row cell b with rightwards arrow on top end cell equals cell 3 i with rightwards arrow on top plus 8 j with rightwards arrow on top end cell row cell c with rightwards arrow on top end cell equals cell 4 i with rightwards arrow on top minus y j with rightwards arrow on top end cell end table

Jika a with rightwards arrow on top times b with rightwards arrow on top equals open vertical bar c with rightwards arrow on top close vertical bar, maka tentukan nilai y.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open vertical bar c with rightwards arrow on top close vertical bar end cell row cell open parentheses table row cell negative 8 end cell row 4 end table close parentheses times open parentheses table row 3 row 8 end table close parentheses end cell equals cell square root of 4 squared plus open parentheses negative y close parentheses squared end root end cell row cell open parentheses negative 8 close parentheses times 3 plus 4 times 8 end cell equals cell square root of 16 plus y squared end root end cell row cell negative 24 plus 32 end cell equals cell square root of 16 plus y squared end root end cell row cell 8 squared end cell equals cell open parentheses square root of 16 plus y squared end root close parentheses squared end cell row 64 equals cell 16 plus y squared end cell row 48 equals cell y squared end cell row cell y squared end cell equals 48 row y equals cell plus-or-minus square root of 48 end cell row y equals cell plus-or-minus square root of 16 times 3 end root end cell row y equals cell plus-or-minus 4 square root of 3 end cell end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table.

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