Roboguru

Dua vektor  membentuk suatu sudut . Nilai cosinus  adalah...

Pertanyaan

Dua vektor top enclose a equals open parentheses table row 15 row cell negative 3 end cell end table close parentheses space dan space top enclose b equals open parentheses table row cell negative 5 end cell row 1 end table close parentheses membentuk suatu sudut theta. Nilai cosinus theta adalah...

  1. negative 1 half 

  2. negative 1 

  3. 0 

  4. 1 half 

  5. 1 

Pembahasan Soal:

Menentukan top enclose a times top enclose b 

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose a times top enclose b end cell equals cell 15 cross times left parenthesis negative 5 right parenthesis plus left parenthesis negative 3 right parenthesis cross times 1 end cell row blank equals cell negative 75 minus 3 end cell row blank equals cell negative 78 end cell end table  

Menentukan vertical line top enclose a vertical line space dan vertical line top enclose b vertical line

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line top enclose a vertical line end cell equals cell square root of 15 squared plus left parenthesis negative 3 right parenthesis squared end root end cell row blank equals cell square root of 225 plus 9 end root end cell row blank equals cell square root of 234 end cell row blank equals cell square root of 9 cross times 26 end root end cell row blank equals cell 3 square root of 26 end cell row cell vertical line top enclose b vertical line end cell equals cell square root of left parenthesis negative 5 right parenthesis squared plus 1 squared end root end cell row blank equals cell square root of 25 plus 1 end root end cell row blank equals cell square root of 26 end cell end table   

Menentukan cosinus theta

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator top enclose a times top enclose b over denominator vertical line top enclose a vertical line times vertical line top enclose b vertical line end fraction end cell row blank equals cell fraction numerator negative 78 over denominator 3 square root of 26 cross times square root of 26 end fraction end cell row blank equals cell fraction numerator negative 78 over denominator 3 cross times 26 end fraction end cell row blank equals cell fraction numerator negative 78 over denominator 78 end fraction end cell row blank equals cell negative 1 end cell end table 

Jadi, jawaban yang benar adalah B.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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