Roboguru

Misalkan  dengan  sudut antara ,  skalar. Pernyataan berikut yang benar adalah .... Jika  maka         Jika  maka .

Pertanyaan

Misalkan begin mathsize 14px style u with rightwards harpoon with barb upwards on top equals open parentheses u subscript 1 comma space u subscript 2 comma space u subscript 3 close parentheses space dan space v with rightwards harpoon with barb upwards on top equals open parentheses v subscript 1 comma space v subscript 2 comma space v subscript 3 close parentheses end style dengan begin mathsize 14px style theta end style sudut antara begin mathsize 14px style u with rightwards harpoon with barb upwards on top space dan space v with rightwards harpoon with barb upwards on top end stylebegin mathsize 14px style k end style skalar. Pernyataan berikut yang benar adalah ....

  • Jika begin mathsize 14px style u times v end style maka

 begin mathsize 14px style tan space theta equals fraction numerator open double vertical bar u times v close double vertical bar over denominator open parentheses u times v close parentheses end fraction end style 

  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u plus k v right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v 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 u end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v end table end style  
  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u plus v right parenthesis end cell end table times table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u minus v right parenthesis 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis v times u right parenthesis end cell end table end style 
  • Jika begin mathsize 14px style u times v equals 0 end style maka begin mathsize 14px style u equals 0 space atau space v equals 0 end style.

Pembahasan Soal:

Perhatikan

  • Jika begin mathsize 14px style u times v end style maka

 begin mathsize 14px style tan space theta equals fraction numerator open double vertical bar u times v close double vertical bar over denominator open parentheses u times v close parentheses end fraction end style 

Pernyataan di atas salah karena,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator open parentheses u times v close parentheses over denominator open double vertical bar u times v close double vertical bar end fraction end cell row cell fraction numerator 1 over denominator cos space theta end fraction end cell equals cell fraction numerator open double vertical bar u times v close double vertical bar over denominator open parentheses u times v close parentheses end fraction end cell row cell space sec space theta end cell equals cell fraction numerator open double vertical bar u times v close double vertical bar over denominator open parentheses u times v close parentheses end fraction end cell end table end style

  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u plus k v right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v 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 u end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v end table end style  

Pernyataan di atas salah karena,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u plus k v right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table u times v plus k open parentheses v times v close parentheses end style

  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u plus v right parenthesis end cell end table times table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u minus v right parenthesis 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis v times u right parenthesis end cell end table end style 

Pernyataan di atas salah karena,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u plus v right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis u minus v right parenthesis 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 u end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank u end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank v end table end style 

  • Jika begin mathsize 14px style u times v equals 0 end style maka begin mathsize 14px style u equals 0 space atau space v equals 0 end style.

Pernyataan di atas benar berdasarkan sifat-sifat perkalian titik vektor.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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