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Pertanyaan

Diketahui titik-titik A ( 1 , − 3 , 2 ) , B ( 1 , 3 , 10 ) dan C ( 4 , − 1 , 8 ) . Jika D merupakan proyeksi titik C pada garis AB maka AD sama dengan ...

Diketahui titik-titik  dan . Jika  merupakan proyeksi titik  pada garis  maka  sama dengan ...

  1. 36 stack text i end text with rightwards arrow on top plus 48 stack text j end text with rightwards arrow on top 

  2. stack text i end text with rightwards arrow on top plus 36 stack text j end text with rightwards arrow on top minus 48 stack text k end text with rightwards arrow on top 

  3. stack text i end text with rightwards arrow on top plus 36 stack text j end text with rightwards arrow on top plus 48 stack text k end text with rightwards arrow on top 

  4. 36 stack text j end text with rightwards arrow on top plus 48 stack text k end text with rightwards arrow on top 

  5. 36 stack text j end text with rightwards arrow on top minus 48 stack text k end text with rightwards arrow on top 

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

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Pembahasan

Panjang vektor , yaitu Jika vektor dan , maka Proyeksi vektor orthogonal vektor pada dapat ditentukan menggunakan rumus berikut. Komponen vektor dan dapat ditentukan sebagai berikut. Proyeksi vektor pada adalah sebagai berikut. Diperoleh vektor Oleh karena itu, tidak terdapat pilihan jawaban yang tepat.

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

Proyeksi vektor orthogonal vektor a with rightwards arrow on top pada b with rightwards arrow on top dapat ditentukan menggunakan rumus berikut.

c with rightwards arrow on top 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 squared end fraction times b with rightwards arrow on top

Komponen vektor stack A C with rightwards arrow on top dan stack A B with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A C with rightwards arrow on top end cell equals cell text C-A end text end cell row blank equals cell open parentheses table row 4 row cell negative 1 end cell row 8 end table close parentheses minus open parentheses table row 1 row cell negative 3 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 2 row 6 end table close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell text B-A end text end cell row blank equals cell open parentheses table row 1 row 3 row 10 end table close parentheses minus open parentheses table row 1 row cell negative 3 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row 0 row 6 row 8 end table close parentheses end cell end table

Proyeksi vektor stack A C with rightwards harpoon with barb upwards on top pada stack A B with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A D with rightwards arrow on top end cell equals cell fraction numerator stack A C with rightwards arrow on top times stack A B with rightwards arrow on top over denominator open vertical bar stack A B with rightwards arrow on top close vertical bar squared end fraction times stack A B with rightwards arrow on top end cell row blank equals cell fraction numerator open parentheses table row 3 row 2 row 6 end table close parentheses open parentheses table row 0 row 6 row 8 end table close parentheses over denominator open parentheses square root of 0 squared plus 6 squared plus 8 squared end root close parentheses squared end fraction times open parentheses table row 0 row 6 row 8 end table close parentheses end cell row blank equals cell fraction numerator 3 times 0 plus 2 times 6 plus 6 times 8 over denominator open parentheses square root of 100 close parentheses squared end fraction times open parentheses table row 0 row 6 row 8 end table close parentheses end cell row blank equals cell 60 over 100 times open parentheses table row 0 row 6 row 8 end table close parentheses end cell row blank equals cell 3 over 5 times open parentheses table row 0 row 6 row 8 end table close parentheses end cell row blank equals cell times open parentheses table row 0 row cell 18 over 5 end cell row cell 24 over 5 end cell end table close parentheses end cell end table

Diperoleh vektor stack A D with rightwards arrow on top equals 18 over 5 j with rightwards arrow on top plus 24 over 5 k with rightwards arrow on top 

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