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Diketahui vektor a=9i−2j​+4k dan vektor b=2i+2j​+k. Proyeksi ortogonal vektor a pada b adalah ....

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals 9 i with hat on top minus 2 j with hat on top plus 4 k with hat on top space dan space vekto r space b with rightwards arrow on top equals 2 i with hat on top plus 2 j with hat on top plus k with hat on top. Proyeksi ortogonal vektor stack straight a space with rightwards arrow on top pada space b with rightwards arrow on top adalah ....

  1. negative 4 i with hat on top minus 4 j with hat on top plus 4 k with hat on top  

  2. 2 i with hat on top plus 2 j with hat on top plus 4 k with hat on top  

  3. 4 i with hat on top plus 4 j with hat on top plus 2 k with hat on top  

  4. 8 i with hat on top plus 8 j with hat on top plus 4 k with hat on top   

  5. 18 i with hat on top minus 4 j with hat on top plus 8 k with hat on top  

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.  

Pembahasan

Ingat konsep operasi perkalian titik pada vektor :

table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top. q with rightwards arrow on top end cell equals cell open parentheses table row cell p subscript 1 end cell row cell p subscript 2 end cell row cell... end cell row cell p subscript n end cell end table close parentheses. open parentheses table row cell q subscript 1 end cell row cell q subscript 2 end cell row cell... end cell row cell q subscript n end cell end table close parentheses. end cell row blank equals cell p subscript 1 q subscript 1 plus p subscript 2 q subscript 2 plus... plus p subscript n q subscript n end cell end table  

Ingat rumus panjang vektor :

p with rightwards arrow on top equals open parentheses table row cell p subscript 1 end cell row cell p subscript 2 end cell row cell... end cell row cell p subscript n end cell end table close parentheses space maka space open vertical bar p with rightwards arrow on top close vertical bar equals square root of p subscript 1 squared plus p subscript 2 squared plus.... plus p subscript n squared end root  

Ingat konsep perkalian titik dua vektor jika diketahui sudutnya :

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 cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar. cos space theta end cell end table   

Ingat rumus :

table attributes columnalign right center left columnspacing 0px end attributes row cell proyeksi space ortogonal space vektor space a with rightwards arrow on top space pada stack space b with rightwards arrow on top end cell equals cell open parentheses fraction numerator a with rightwards arrow on top. b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar squared end fraction close parentheses. b with rightwards arrow on top end cell end table 

Berdasarkan konsep di atas maka berlaku :

table attributes columnalign right center left columnspacing 0px end attributes row cell proyeksi space ortogonal space vektor space a with rightwards arrow on top space pada stack space b with rightwards arrow on top end cell equals cell open parentheses fraction numerator a with rightwards arrow on top. b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar squared end fraction close parentheses. b with rightwards arrow on top end cell row blank equals cell fraction numerator open parentheses table row 9 row cell negative 2 end cell row 4 end table close parentheses. open parentheses table row 2 row 2 row 1 end table close parentheses over denominator 4 plus 4 plus 1 end fraction. open parentheses table row 2 row 2 row 1 end table close parentheses end cell row blank equals cell 18 over 9. open parentheses table row 2 row 2 row 1 end table close parentheses end cell row blank equals cell 2. open parentheses table row 2 row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 4 row 4 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 i end cell row cell 4 j end cell row cell 2 k end cell end table close parentheses end cell end table 

Oleh karena itu jawaban yang tepat adalah C.  

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veliafitt

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Jawaban terverifikasi

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