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Pertanyaan

Jika u = ⎝ ⎛ ​ 1 2 ​ a ​ ⎠ ⎞ ​ ; v = ⎝ ⎛ ​ 1 − 2 ​ a ​ ⎠ ⎞ ​ , dan ∠ ( u , v ) = 3 π ​ , maka tentukanlah nilai a yang memenuhi ..

Jika , dan, maka tentukanlah nilai a yang memenuhi ..

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

nilai a adalah .

nilai a adalah plus-or-minus square root of 5.

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Pembahasan

Diketahui : Jika , dan , Ditanya : maka tentukanlah nilai a yang memenuhi .. Penyelesaian : Jadi, nilai a adalah .

Diketahui :

Jika u with rightwards arrow on top equals open parentheses table row 1 row cell square root of 2 end cell row a end table close parentheses semicolon space v with rightwards arrow on top equals open parentheses table row 1 row cell negative square root of 2 end cell row a end table close parentheses,

danangle open parentheses u with rightwards arrow on top comma space v with rightwards arrow on top close parentheses equals straight pi over 3,

Ditanya :

maka tentukanlah nilai a yang memenuhi ..

Penyelesaian :

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator u with rightwards arrow on top. space top enclose v over denominator open vertical bar u close vertical bar open vertical bar v close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row 1 row cell square root of 2 end cell row a end table close parentheses open parentheses table row 1 row cell negative square root of 2 end cell row a end table close parentheses over denominator square root of 1 squared plus open parentheses square root of 2 close parentheses squared plus a squared end root square root of 1 squared plus open parentheses negative square root of 2 close parentheses squared plus a squared end root end fraction end cell row blank equals cell fraction numerator 1 minus 2 plus a squared over denominator 3 plus a squared end fraction end cell row blank equals cell fraction numerator negative 1 plus a squared over denominator 3 plus a squared end fraction end cell row cell cos space 180 over 30 end cell equals cell cos space 60 end cell row blank equals cell 1 half end cell row cell 1 half end cell equals cell fraction numerator negative 1 plus a squared over denominator 3 plus a squared end fraction end cell row cell 3 plus a squared end cell equals cell negative 2 plus 2 a squared end cell row 5 equals cell a squared end cell row cell plus-or-minus square root of 5 end cell equals a end table

Jadi, nilai a adalah plus-or-minus square root of 5.

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