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Jika sudut antara vektor m⇀=i⇀+2​j⇀​+rk⇀dann⇀=i⇀−2​j⇀​+rk⇀ adalah 60∘ maka r adalah....

Pertanyaan

Jika sudut antara vektor straight m with rightwards harpoon with barb upwards on top equals straight i with rightwards harpoon with barb upwards on top plus square root of 2 straight j with rightwards harpoon with barb upwards on top plus straight r straight k with rightwards harpoon with barb upwards on top space dan space straight n with rightwards harpoon with barb upwards on top equals straight i with rightwards harpoon with barb upwards on top minus square root of 2 straight j with rightwards harpoon with barb upwards on top plus straight r straight k with rightwards harpoon with barb upwards on top adalah 60 degree maka r adalah....

  1. negative 1 half space atau space 1 half

  2. negative 1 space atau space 1

  3. negative square root of 2 space atau space square root of 2

  4. negative square root of 5 space atau space square root of 5

  5. negative 1 half square root of 5 space atau space 1 half square root of 5

Pembahasan:

Mencari nilai straight m. straight n

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m. straight n end cell equals cell open parentheses straight i with rightwards harpoon with barb upwards on top plus square root of 2 straight j with rightwards harpoon with barb upwards on top plus straight r straight k with rightwards harpoon with barb upwards on top close parentheses. open parentheses straight i with rightwards harpoon with barb upwards on top minus square root of 2 straight j with rightwards harpoon with barb upwards on top plus straight r straight k with rightwards harpoon with barb upwards on top close parentheses end cell row blank equals cell 1 minus 2 plus straight r squared end cell row blank equals cell negative 1 plus straight r squared end cell end table

Mencari nilai open vertical bar straight m close vertical bar. open vertical bar straight n close vertical bar

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight m close vertical bar. open vertical bar straight n close vertical bar end cell equals cell square root of 1 plus 2 plus straight r squared end root. square root of 1 plus 2 plus straight r squared end root end cell row blank equals cell square root of 3 plus straight r squared end root. square root of 3 plus straight r squared end root end cell row blank equals cell 3 plus straight r squared end cell end table

Makamencari nilai r dari vektor diatas adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight m. straight n over denominator open vertical bar straight m close vertical bar. open vertical bar straight n close vertical bar end fraction cross times cos space 60 degree end cell equals cell fraction numerator negative 1 plus straight r squared over denominator 3 plus straight r squared end fraction cross times 1 half end cell row cell 2 open parentheses negative 1 plus straight r squared close parentheses end cell equals cell 1 open parentheses 3 plus straight r squared close parentheses end cell row cell negative 2 plus 2 straight r squared end cell equals cell 3 plus straight r squared end cell row cell negative 2 minus 3 end cell equals cell straight r squared minus 2 straight r squared end cell row cell negative 5 end cell equals cell negative straight r squared end cell row cell plus-or-minus square root of 5 end cell equals straight r end table

Oleh karena itu jawabannya adalah D

 

Jawaban terverifikasi

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 06 Oktober 2021

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