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Jika a=(x,4,7) dan b (6,y,14) segaris,maka nilai x-y =

Pertanyaan

Jika a=(x,4,7) dan b (6,y,14) segaris,maka nilai x-y =

Pembahasan Soal:

Mencari nilai x dan y serta nilai k

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards harpoon with barb upwards on top end cell equals cell straight k. straight b with rightwards harpoon with barb upwards on top end cell row cell open parentheses table row straight x row 4 row 7 end table close parentheses end cell equals cell straight k open parentheses table row 6 row straight y row 14 end table close parentheses end cell row straight x equals cell 6 straight k end cell row 4 equals ky row 7 equals cell 14 straight k rightwards arrow 1 half equals straight k end cell end table

Subsitusi ke x dan y

table attributes columnalign right center left columnspacing 0px end attributes row straight x equals cell 6 cross times 1 half end cell row blank equals 3 row 4 equals yk row 4 equals cell straight y cross times 1 half end cell row 8 equals straight y end table

Maka x-y adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight x minus straight y end cell equals cell 3 minus 8 end cell row blank equals cell negative 5 end cell end table

Jadi hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell straight x minus straight y end cell equals cell negative 5 end cell end table

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 06 Juni 2021

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Pertanyaan yang serupa

Titik , , dan  segaris, nilai  adalah ....

Pembahasan Soal:

Jika tiga titik A, B, dan C segaris (kolinear), maka berlaku begin mathsize 14px style AB with rightwards arrow on top equals k times AC with rightwards arrow on top end style dengan begin mathsize 14px style k end style adalah konstanta.
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell k times AC with rightwards arrow on top end cell row cell left parenthesis negative 3 comma 1 comma n plus 2 right parenthesis minus left parenthesis 2 comma 0 comma 3 right parenthesis end cell equals cell k times open parentheses left parenthesis m comma negative 2 comma negative 1 right parenthesis minus left parenthesis 2 comma 0 comma 3 right parenthesis close parentheses end cell row cell left parenthesis negative 5 comma 1 comma n minus 1 right parenthesis end cell equals cell k times left parenthesis m minus 2 comma negative 2 comma negative 4 right parenthesis end cell row cell left parenthesis negative 5 comma 1 comma n minus 1 right parenthesis end cell equals cell left parenthesis left parenthesis m minus 2 right parenthesis k comma negative 2 k comma negative 4 k right parenthesis end cell end table end style 

Didapat:
 

  •  begin mathsize 14px style 1 equals negative 2 k k equals negative 1 half end style

     
  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 5 end cell equals cell left parenthesis m minus 2 right parenthesis k end cell row cell negative 5 end cell equals cell left parenthesis m minus 2 right parenthesis times left parenthesis negative 1 half right parenthesis end cell row cell negative 10 end cell equals cell 2 minus m end cell row m equals 12 row blank blank blank end table end style 

     
  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell n minus 1 end cell equals cell negative 4 k end cell row cell n minus 1 end cell equals cell negative 4 times left parenthesis negative 1 half right parenthesis end cell row cell n minus 1 end cell equals 2 row n equals 3 end table end style
     

Didapat nilai begin mathsize 14px style m equals 12 space dan space n equals 3 end style, sehingga:
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m minus 4 n end cell equals cell 12 minus 4 times 3 end cell row blank equals cell 12 minus 12 end cell row blank equals 0 end table end style
 

Oleh karena itu, jawaban yang benar adalah C.

Roboguru

Diketahui dua vektor  dan   terletak pada satu garis. Nilai  adalah

Pembahasan Soal:

straight a with bar on top space dan space straight b with bar on top space koliner( berada pada satu garis), maka straight a with bar on top. straight k equals straight b with bar on top.

open parentheses table row 4 row 3 end table close parentheses straight k equals open parentheses table row straight n row 12 end table close parentheses

Dari kesamaan dua vektor diatas, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 straight k end cell equals 12 row straight k equals 4 end table

  • menentukan nilai straight n:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 straight k end cell equals straight n row cell 4 left parenthesis 4 right parenthesis end cell equals straight n row 16 equals straight n row straight n equals 16 end table

Oleh karena itu, jawaban yang benar adalah D.

 

 

Roboguru

Diketahui  dan . Jika  dan  segaris (kolinear) maka  adalah...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell open square brackets table row 3 row 3 row 1 end table close square brackets minus open square brackets table row 1 row 2 row 3 end table close square brackets end cell row cell stack A B with rightwards arrow on top end cell equals cell open square brackets table row 2 row 1 row cell negative 2 end cell end table close square brackets end cell row cell stack B C with rightwards arrow on top end cell equals cell open square brackets table row 7 row 5 row cell negative 3 end cell end table close square brackets minus open square brackets table row 3 row 3 row 1 end table close square brackets end cell row cell stack B C with rightwards arrow on top end cell equals cell open square brackets table row 4 row 2 row cell negative 4 end cell end table close square brackets end cell end table end style 

Karena segaris, maka;

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack B C with rightwards arrow on top end cell equals cell k stack A B with rightwards arrow on top end cell row cell open square brackets table row 4 row 2 row cell negative 4 end cell end table close square brackets end cell equals cell k open square brackets table row 2 row 1 row cell negative 2 end cell end table close square brackets end cell row blank rightwards double arrow cell 4 equals 2 k end cell row k equals 2 end table end style 

sehingga,

begin mathsize 14px style stack A B space with rightwards arrow on top colon space stack B C with rightwards arrow on top equals 1 space colon space 2 end style 

Jadi, jawaban yang tepat adalah A.

Roboguru

Titik ,  dan  segaris, serta ; . Kalau  maka  adalah ...

Pembahasan Soal:

Apabila diketahui vektor posisi stack O A with rightwards arrow on top equals a with rightwards arrow on top dan stack O B with rightwards arrow on top equals b with rightwards arrow on top, maka stack A B with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top

Jika titik text A end texttext B end texttext C end text segaris dan m sebuah bilangan, maka berlaku:

stack A B with rightwards arrow on top equals m stack A C with rightwards arrow on top

Misal titik text Q end text open parentheses x comma space y close parentheses

Jika text PQ=QR end text, maka dapat ditentukan hubungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards arrow on top end cell equals cell stack Q R with rightwards arrow on top end cell row cell q with rightwards arrow on top minus p with rightwards arrow on top end cell equals cell r with rightwards arrow on top minus q with rightwards arrow on top end cell row cell open parentheses table row x row y end table close parentheses minus open parentheses table row cell negative 2 end cell row 2 end table close parentheses end cell equals cell open parentheses table row 6 row 10 end table close parentheses minus open parentheses table row x row y end table close parentheses end cell row cell open parentheses table row cell x plus 2 end cell row cell y minus 2 end cell end table close parentheses end cell equals cell open parentheses table row cell 6 minus x end cell row cell 10 minus y end cell end table close parentheses end cell end table

Berdasarkan kesamaan di atas, nilai x dan y adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 end cell equals cell 6 minus x end cell row cell 2 x end cell equals 4 row x equals 2 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 2 end cell equals cell 10 minus y end cell row cell 2 y end cell equals 12 row y equals 6 end table

Diperoleh titik text Q end text open parentheses 2 comma space 6 close parentheses 

Oleh karena itu, jawaban yang tepat adalah E.

Roboguru

Diketahui , , dan . Jika A, B, dan C segaris (kolinier), perbandingan  adalah ....

Pembahasan Soal:

Karena titik A, B, dan C segaris (kolinier), maka berlaku:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell k times stack B C with rightwards arrow on top end cell row cell stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell equals cell k times open parentheses stack O C with rightwards arrow on top minus stack O B with rightwards arrow on top close parentheses end cell row cell open parentheses table row 3 row 3 row 1 end table close parentheses minus open parentheses table row 1 row 2 row 3 end table close parentheses end cell equals cell k times open parentheses open parentheses table row 7 row 5 row cell negative 3 end cell end table close parentheses minus open parentheses table row 3 row 3 row 1 end table close parentheses close parentheses end cell row cell open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses end cell equals cell k open parentheses table row 4 row 2 row cell negative 4 end cell end table close parentheses end cell row 2 equals cell 4 k end cell row k equals cell 1 half end cell end table end style 

Diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell k times BC with rightwards arrow on top end cell row cell AB with rightwards arrow on top end cell equals cell 1 half times BC with rightwards arrow on top end cell row cell fraction numerator AB with rightwards arrow on top over denominator BC with rightwards arrow on top end fraction end cell equals cell 1 half end cell row cell AB with rightwards arrow on top space colon space BC with rightwards arrow on top end cell equals cell 1 space colon space 2 end cell end table end style 

Jadi, perbandingan begin mathsize 14px style AB with rightwards arrow on top space colon space BC with rightwards arrow on top end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px colon end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 2 end table.

Dengan demikian, jawaban yang tepat adalah A.

Roboguru

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