Roboguru

Pertanyaan

Dua vektor a dan b memiliki nilai titik tangkap yang sama dan nilai yang sama pula. Jika sudut apit antara kedua vektor adalah β maka berlaku hubungan:

|a+b| = 2|a-b|

maka cos β adalah ….

  1. 1/2 space

  2. 1/3space 

  3. 1/6space 

  4. 1/4space 

  5. 1/5space 

Y. Maghfirah

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui:

vertical line straight a plus straight b vertical line space equals space 2 vertical line straight a minus straight b vertical line

Ditanyakan : cos space beta

Jawab:

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line straight a plus straight b vertical line space end cell equals cell space 2 vertical line straight a minus straight b vertical line end cell row cell square root of straight a squared plus straight b squared plus 2. straight a. straight b. cos space beta end root end cell equals cell 2 square root of straight a squared plus straight b squared minus 2. straight a. straight b. cos space beta end root end cell row cell straight a squared plus straight b squared plus 2. straight a. straight b. cos space beta end cell equals cell 4 open parentheses straight a squared plus straight b squared minus 2. straight a. straight b. cos space beta close parentheses end cell row cell straight a squared plus straight b squared plus 2. straight a. straight b. cos space beta end cell equals cell 4 straight a squared plus 4 straight b squared minus 8. straight a. straight b. cos space beta end cell row cell karena space straight a end cell equals straight b row cell straight a squared plus straight a squared plus 2. straight a. straight a. cos space beta end cell equals cell 4 straight a squared plus 4 straight a squared minus 8. straight a. straight a. cos space beta end cell row cell 2 straight a squared plus 2 straight a squared cos space beta end cell equals cell 8 straight a squared minus 8 straight a squared cos space beta end cell row cell 2 straight a squared cos space beta plus 8 straight a squared cos space beta end cell equals cell 8 straight a squared minus 2 straight a squared end cell row cell 10 straight a squared cos space beta end cell equals cell 6 straight a squared end cell row cell cos space beta end cell equals cell 6 over 10 end cell row cell cos space beta end cell equals cell 3 over 5 end cell end table  

oleh karena itu cos β adalah 3/5. Tidak ada jawaban yang tepat.

1rb+

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