Diberikan dua buah vektor a⇀=−i⇀+j⇀​+pk⇀, p>0 dan b⇀=3i⇀−3j⇀​. Jika ∣∣​a⇀∣∣​=∣∣​b⇀∣∣​ , maka carilah vektor satuan a⇀ dan (a⇀−b⇀).

Pertanyaan

Diberikan dua buah vektor begin mathsize 14px style a with rightwards harpoon with barb upwards on top equals negative i with rightwards harpoon with barb upwards on top plus j with rightwards harpoon with barb upwards on top plus p k with rightwards harpoon with barb upwards on top end stylebegin mathsize 14px style p greater than 0 space d a n space b with rightwards harpoon with barb upwards on top equals 3 i with rightwards harpoon with barb upwards on top minus 3 j with rightwards harpoon with barb upwards on top end style. Jika undefined , maka carilah vektor satuan size 14px a with size 14px rightwards harpoon with barb upwards on top dan begin mathsize 14px style open parentheses a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top close parentheses end style.

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Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Perhatikan 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open parentheses negative 1 close parentheses squared plus 1 squared plus p squared end root end cell row cell open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 2 plus p squared end root end cell row cell open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open parentheses 3 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row cell open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 18 end cell row cell open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar end cell row cell square root of 2 plus p squared end root end cell equals cell square root of 18 end cell row cell 2 plus p squared end cell equals 18 row cell p squared end cell equals 16 row p equals cell plus-or-minus 4 end cell end table end style 

  • begin mathsize 14px style p equals 4 end style , begin mathsize 14px style a with rightwards harpoon with barb upwards on top equals left parenthesis negative 1 comma space 1 comma space 4 right parenthesis comma space vektor space satuan space a with rightwards harpoon with barb upwards on top equals 3 square root of 2 open parentheses negative 1 comma space 1 comma space 4 close parentheses end style 
  • size 14px p size 14px equals size 14px minus size 14px 4 , begin mathsize 14px style a with rightwards harpoon with barb upwards on top equals left parenthesis negative 1 comma space 1 comma space minus 4 right parenthesis comma space vektor space satuan space a with rightwards harpoon with barb upwards on top equals 3 square root of 2 open parentheses negative 1 comma space 1 comma space minus 4 close parentheses end style 

186

5.0 (2 rating)

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