Roboguru

Diketahui koordinat A(6,-2,-6), B(3,4,6) dan C(9,x,y). Jika titik-titik A,B dan C koliner (segaris), maka nilai x-y sama dengan ....

Pertanyaan

Diketahui koordinat A(6,-2,-6), B(3,4,6) dan C(9,x,y). Jika titik-titik A,B dan C koliner (segaris), maka nilai x-y sama dengan ....space space space space 

  1. begin mathsize 14px style negative 18 end style 

  2. begin mathsize 14px style 4 end style 

  3. begin mathsize 14px style 6 end style 

  4. begin mathsize 14px style 10 end style 

  5. begin mathsize 14px style 18 end style 

Pembahasan Soal:

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 space stack A C with rightwards arrow on top end cell row cell open parentheses table row 3 row 4 row 6 end table close parentheses minus open parentheses table row 6 row cell negative 2 end cell row cell negative 6 end cell end table close parentheses end cell equals cell k. open parentheses open parentheses table row 3 row 4 row 6 end table close parentheses minus open parentheses table row 9 row x row y end table close parentheses close parentheses end cell row cell open parentheses table row cell negative 3 end cell row 6 row 12 end table close parentheses end cell equals cell k open parentheses table row cell negative 6 end cell row cell 4 minus x end cell row cell 6 minus y end cell end table close parentheses end cell row blank blank blank end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 end cell equals cell k. negative 6 end cell row k equals cell 1 half end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row 6 equals cell 1 half left parenthesis 4 minus x right parenthesis end cell row 12 equals cell 4 minus x end cell row x equals cell negative 8 end cell row blank blank blank row 12 equals cell 1 half left parenthesis 6 minus y right parenthesis end cell row 24 equals cell 6 minus y end cell row y equals cell negative 18 end cell row blank blank blank end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus y end cell equals cell negative 8 minus left parenthesis negative 18 right parenthesis end cell row blank equals 10 end table 

 

Jadi jawaban yang tepat adalah D

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Septianingsih

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 03 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Gambarlah vektor dengan titik P(2,-3,1) dan Q(1,3,-2) b. Buat vektor negatif dari , kemudian hitung modulusnya/besarnya !

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative stack P Q with rightwards arrow on top end cell equals cell negative open square brackets open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell row 1 end table close parentheses close square brackets end cell row blank equals cell negative open parentheses table row cell negative 1 end cell row 6 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 row cell negative 6 end cell row 3 end table close parentheses end cell end table 

Modulus

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell square root of 1 squared plus negative 6 squared plus 3 squared end root end cell row blank equals cell square root of 1 plus 6 plus 9 end root end cell row blank equals 4 end table 

Roboguru

Vektor posisi A, B, dan C terhadap titik O secara berturut-turut adalah , , dan . Jika titik A, B, dan C segaris, maka  adalah ....

Pembahasan Soal:

Perhatikan bahwa

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 stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row blank equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell row blank equals cell open parentheses 3 u with rightwards arrow on top plus 4 v with rightwards arrow on top plus w with rightwards arrow on top close parentheses minus open parentheses u with rightwards arrow on top plus v with rightwards arrow on top plus 2 w with rightwards arrow on top close parentheses end cell row blank equals cell 3 u with rightwards arrow on top plus 4 v with rightwards arrow on top plus w with rightwards arrow on top minus u with rightwards arrow on top minus v with rightwards arrow on top minus 2 w with rightwards arrow on top end cell row blank equals cell 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top minus w with rightwards arrow on top end cell end table end style

dan

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 stack O C with rightwards arrow on top minus stack O B with rightwards arrow on top end cell row blank equals cell c with rightwards arrow on top minus b with rightwards arrow on top end cell row blank equals cell open parentheses 9 u with rightwards arrow on top plus 13 v with rightwards arrow on top minus 2 w with rightwards arrow on top close parentheses minus open parentheses 3 u with rightwards arrow on top plus 4 v with rightwards arrow on top plus w with rightwards arrow on top close parentheses end cell row blank equals cell 9 u with rightwards arrow on top plus 13 v with rightwards arrow on top minus 2 w with rightwards arrow on top minus 3 u with rightwards arrow on top minus 4 v with rightwards arrow on top minus w with rightwards arrow on top end cell row blank equals cell 6 u with rightwards arrow on top plus 9 v with rightwards arrow on top minus 3 w with rightwards arrow on top end cell row blank equals cell 3 open parentheses 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top minus w with rightwards arrow on top close parentheses end cell row blank equals cell 3 stack A B with rightwards arrow on top end cell end table end style

Sehinga

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 3 stack A B with rightwards arrow on top end cell row cell fraction numerator stack B C with rightwards arrow on top over denominator stack A B with rightwards arrow on top end fraction end cell equals cell 3 over 1 end cell end table end style

Maka begin mathsize 14px style stack B C with rightwards arrow on top colon stack A B with rightwards arrow on top equals 3 colon 1 end style. Akibatnya, begin mathsize 14px style stack A B with rightwards arrow on top colon stack B C with rightwards arrow on top equals 1 colon 3 end style

Roboguru

Gambarlah vektor dengan titik P(2,-3,1) dan Q(1,3,-2) a. Hitung modulus vektor

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards arrow on top end cell equals cell open square brackets open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell row 1 end table close parentheses close square brackets end cell row blank equals cell open parentheses table row cell negative 1 end cell row 6 row cell negative 3 end cell end table close parentheses end cell row blank blank blank end table  

Modulus

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell square root of open parentheses negative 1 close parentheses squared plus 6 squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 1 plus 6 plus 9 end root end cell row blank equals 4 end table  

Roboguru

Diketahui vektor  Jika  tegak lurus  maka  adalah ....

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top. b with rightwards arrow on top end cell equals 0 row cell open parentheses table row 1 row cell negative x end cell row 3 end table close parentheses. open parentheses table row 2 row 1 row cell negative 1 end cell end table close parentheses end cell equals 0 row cell 2 minus x minus 3 end cell equals 0 row cell negative x minus 1 end cell equals 0 row x equals cell negative 1 end cell end table 

 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 a with rightwards arrow on top left parenthesis b with rightwards arrow on top minus c with rightwards arrow on top right parenthesis end cell row blank equals cell 2 open parentheses table row 1 row cell negative 1 end cell row 3 end table close parentheses open square brackets open parentheses table row 2 row 1 row cell negative 1 end cell end table close parentheses minus open parentheses table row 1 row 3 row 2 end table close parentheses close square brackets end cell row blank equals cell open parentheses table row 2 row cell negative 2 end cell row 6 end table close parentheses open parentheses table row 1 row cell negative 2 end cell row 1 end table close parentheses end cell row blank equals cell 2 plus 2 plus 6 end cell row blank equals 10 end table 

 

Jadi jawaban yang tepat adalah C

Roboguru

Jika  dan titik  maka koordinat titik  adalah...

Pembahasan Soal:

Diketahui:

 top enclose PQ equals open parentheses table row 3 row 5 row 1 end table close parentheses space dan space top enclose PR equals open parentheses table row 4 row 1 row 2 end table close parentheses  

straight Q left parenthesis 1 comma space 3 comma space minus 2 right parenthesis

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose PQ end cell equals cell straight q with rightwards arrow on top minus straight p with rightwards arrow on top end cell row cell open parentheses table row 3 row 5 row 1 end table close parentheses end cell equals cell open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus straight p with rightwards arrow on top end cell row cell straight p with rightwards arrow on top end cell equals cell open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row 3 row 5 row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell negative 2 end cell row cell negative 3 end cell end table close parentheses end cell end table

Jadi, koordinat titik straight R adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose PR end cell equals cell straight r with rightwards arrow on top minus straight p with rightwards arrow on top end cell row cell open parentheses table row 4 row 1 row 2 end table close parentheses end cell equals cell straight r with rightwards arrow on top minus open parentheses table row cell negative 2 end cell row cell negative 2 end cell row cell negative 3 end cell end table close parentheses end cell row cell straight r with rightwards arrow on top end cell equals cell open parentheses table row 4 row 1 row 2 end table close parentheses plus open parentheses table row cell negative 2 end cell row cell negative 2 end cell row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell end table


Oleh karena itu, jawaban yang benar adalah A.

Roboguru

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