Roboguru

Jarak titik ke titik adalah ....

Pertanyaan

Jarak titik A left parenthesis 4 comma 6 comma 2 right parenthesis ke titik B left parenthesis 3 comma 4 comma 4 right parenthesis adalah ....

  1. 7

  2. 4

  3. 6

  4. 5

  5. 3

Pembahasan Soal:

Jarak titik ke titik

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of open parentheses x subscript A minus x subscript B close parentheses squared plus open parentheses y subscript A minus y subscript B close parentheses squared plus open parentheses z subscript A minus z subscript B close parentheses squared end root end cell row blank equals cell square root of open parentheses 4 minus 3 close parentheses squared plus open parentheses 6 minus 4 close parentheses squared plus open parentheses 2 minus 4 close parentheses squared end root end cell row blank equals cell square root of 1 squared plus 2 squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 1 plus 4 plus 4 end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table

Jadi, jarak titik A left parenthesis 4 comma 6 comma 2 right parenthesis ke titik B left parenthesis 3 comma 4 comma 4 right parenthesis adalah 3.

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Umi

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Juni 2021

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Pertanyaan yang serupa

Tentukan modulus dari vektor-vektor berikut. b.  dengan titik  dan titik B

Pembahasan Soal:

Vektor begin mathsize 14px style stack A B with rightwards arrow on top end style dapat ditentukan sebagai berikut.

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 B minus A end cell row blank equals cell open parentheses table row 2 row 1 row cell negative 4 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 2 end cell row cell negative 3 end cell end table close parentheses end cell end table end style

Modulus vektor tersebut dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack A B with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 4 squared plus open parentheses negative 2 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 16 plus 4 plus 9 end root end cell row blank equals cell square root of 29 end cell end table end style

Dengan demikian, modulus vektor begin mathsize 14px style stack A B with rightwards arrow on top end style adalah begin mathsize 14px style square root of 29 end style 

0

Roboguru

Tentukan modulus dari vektor-vektor berikut. b.    dengan titik  dan titik .

Pembahasan Soal:

begin mathsize 14px style stack A B with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top end style 

     begin mathsize 14px style equals open parentheses table row 2 row 1 row cell negative 4 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses equals open parentheses table row 4 row cell negative 2 end cell row cell negative 3 end cell end table close parentheses end style 

Modulus artinya panjang vektor.

begin mathsize 14px style open vertical bar stack A B with rightwards arrow on top close vertical bar equals square root of 4 squared plus open parentheses negative 2 close parentheses squared plus open parentheses negative 3 close parentheses squared space end root equals square root of 29 end style 

Jadi modulus vektor AB adalah 29.

0

Roboguru

Tentukan modulus dari vektor-vektor berikut. b.  dengan titik  dan titik .

Pembahasan Soal:

Modulus vektor adalah besar atau nilai vektor. Jika diketahui titik begin mathsize 14px style straight A open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses end style dan titik begin mathsize 14px style straight B open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses end style, maka besar nilai vektor begin mathsize 14px style AB with rightwards arrow on top end style adalah 

begin mathsize 14px style AB with rightwards arrow on top equals square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared plus open parentheses z subscript 2 minus z subscript 1 close parentheses squared end root end style .

Akan ditentukan modulus dari begin mathsize 14px style AB with rightwards arrow on top end style dengan titik begin mathsize 14px style straight A open parentheses negative 2 comma space 3 comma space minus 1 close parentheses end style dan titik begin mathsize 14px style straight B open parentheses 2 comma space 1 comma space minus 4 close parentheses end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell AB with rightwards arrow on top end cell equals cell square root of open parentheses 2 minus open parentheses negative 2 close parentheses close parentheses squared plus open parentheses 1 minus 3 close parentheses squared plus open parentheses negative 4 minus open parentheses negative 1 close parentheses close parentheses squared end root end cell row blank equals cell square root of 4 squared plus open parentheses negative 2 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 16 plus 4 plus 9 end root end cell row cell AB with rightwards arrow on top end cell equals cell square root of 29 end cell end table end style  

Jadi, diperoleh modulus dari vektor tersebut adalah begin mathsize 14px style square root of 29 end style.

0

Roboguru

Diketahui vektor  dan  dan panjang proyeksi vektor  pada vektor  adalah . Sudut antara  dan  adalah , maka

Pembahasan Soal:

Panjang vektor a with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top, yaitu open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root

Jika vektor a with rightwards arrow on top equals a subscript 1 i with rightwards arrow on top plus a subscript 2 j with rightwards arrow on top plus a subscript 3 k with rightwards arrow on top dan b with rightwards arrow on top equals b subscript 1 i with rightwards arrow on top plus b subscript 2 j with rightwards arrow on top plus b subscript 3 k with rightwards arrow on top, maka

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3

Jika vektor a with rightwards arrow on top pada vektor b with rightwards arrow on top membentuk sudut alpha, maka berlaku:

a with rightwards arrow on top times b with rightwards arrow on top equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space cos space alpha

Panjang proyeksi vektor a with rightwards arrow on top pada vektor b with rightwards arrow on top dapat ditentukan menggunakan rumus berikut.

open vertical bar c with rightwards arrow on top close vertical bar equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction

Berdasarkan konsep di atas, nilai x dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar c with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row cell 1 over 7 square root of 14 end cell equals cell fraction numerator open parentheses table row x row 1 row 2 end table close parentheses open parentheses table row 2 row 3 row cell negative 1 end cell end table close parentheses over denominator square root of 2 squared plus 3 squared plus open parentheses negative 1 close parentheses squared end root end fraction end cell row cell 1 over 7 square root of 14 end cell equals cell fraction numerator 2 x plus 1 times 3 plus 2 open parentheses negative 1 close parentheses over denominator square root of 4 plus 9 plus 1 end root end fraction end cell row cell 1 over 7 square root of 14 end cell equals cell fraction numerator 2 x plus 1 over denominator square root of 14 end fraction end cell row cell 1 over 7 square root of 14 times square root of 14 end cell equals cell 2 x plus 1 end cell row cell 14 over 7 end cell equals cell 2 x plus 1 end cell row 2 equals cell 2 x plus 1 end cell row cell 2 x end cell equals 1 row x equals cell 1 half end cell end table

Diperoleh x equals 1 half sehingga a with rightwards arrow on top equals open parentheses table row cell 1 half end cell row 1 row 2 end table close parentheses

Nilai cos space alpha adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction times fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of open parentheses begin display style 1 half end style close parentheses squared plus 1 squared plus 2 squared end root end fraction times 1 over 7 square root of 14 end cell row blank equals cell fraction numerator 1 over denominator square root of begin display style 21 over 4 end style end root end fraction times 1 over 7 square root of 14 end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half end style square root of 21 end fraction times 1 over 7 square root of 14 end cell row blank equals cell fraction numerator 2 over denominator square root of 21 end fraction times 1 over 7 square root of 14 end cell row blank equals cell 2 over 21 square root of 6 end cell end table

Oleh karena itu, tidak terdapat pilihan jawaban yang tepat.

0

Roboguru

Diketahui segitiga PQR dengan . Tentukanlah: b. Panjang PQ

Pembahasan Soal:

Diketahui  P left parenthesis 5 comma space 1 comma space 5 right parenthesis comma space Q left parenthesis 1 comma space 4 comma space 5 right parenthesis space dan space R left parenthesis 3 comma space 2 comma space 1 right parenthesis. Maka panajng PQ ditentukan oleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar P Q close vertical bar end cell equals cell square root of open parentheses 1 minus 5 close parentheses squared plus open parentheses 4 minus 1 close parentheses squared plus open parentheses 5 minus 5 close parentheses squared end root end cell row blank equals cell square root of 16 plus 9 plus 0 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table

Jadi, panjang PQ adalah 5 satuan.

0

Roboguru

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