Roboguru

Diketahui  dan  serta . Panjang vektor  adalah

Diketahui begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of 3 end style dan begin mathsize 14px style open vertical bar b with rightwards arrow on top close vertical bar equals 1 end style serta begin mathsize 14px style open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar equals 1 end style. Panjang vektor begin mathsize 14px style open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end style adalah undefined

  1. undefined

  2. begin mathsize 14px style horizontal ellipsis end style

Jawaban:

Diketahui begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of 3 end style dan begin mathsize 14px style open vertical bar b with rightwards arrow on top close vertical bar equals 1 end style serta begin mathsize 14px style open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar equals 1 end style.

Ingatlah bahwa begin mathsize 14px style open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar squared equals open vertical bar a with rightwards arrow on top close vertical bar squared minus 2 a with rightwards arrow on top times b with rightwards arrow on top plus open vertical bar b with rightwards arrow on top close vertical bar squared end style. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared minus 2 a with rightwards arrow on top times b with rightwards arrow on top plus open vertical bar b with rightwards arrow on top close vertical bar squared end cell row cell 1 squared end cell equals cell open parentheses square root of 3 close parentheses squared minus 2 a with rightwards arrow on top times b with rightwards arrow on top plus 1 squared end cell row cell 2 a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell 3 plus 1 minus 1 end cell row cell 2 a with rightwards arrow on top times b with rightwards arrow on top end cell equals 3 end table end style

Selanjutnya karena begin mathsize 14px style vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line squared equals vertical line a with rightwards arrow on top vertical line squared plus 2 a with rightwards arrow on top times b with rightwards arrow on top plus vertical line b with rightwards arrow on top vertical line squared end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus 2 a with rightwards arrow on top times b with rightwards arrow on top plus open vertical bar b with rightwards arrow on top close vertical bar end cell row blank equals cell open parentheses square root of 3 close parentheses squared plus 3 plus 1 squared end cell row blank equals cell 3 plus 3 plus 1 end cell row blank equals 7 row cell square root of vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line squared end root end cell equals cell plus-or-minus square root of 7 end cell row cell vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line end cell equals cell plus-or-minus square root of 7 end cell end table end style

Karena panjang vektor selalu nonnegatif, maka begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line end cell 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 cell square root of 7 end cell end table end style.

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