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Jika vektor a=−4i​+3j​−4k,b=−i​+j​+3k dan c=4i−j​+4k, proyeksi orthogonal vektor a pada (b−c⇀) adalah ...

Pertanyaan

Jika vektor begin mathsize 14px style a with rightwards arrow on top equals stack negative 4 i with rightwards arrow on top plus stack 3 j with rightwards arrow on top minus stack 4 k with rightwards arrow on top comma space b with rightwards arrow on top equals stack negative i with rightwards arrow on top plus j with rightwards arrow on top plus stack 3 k with rightwards arrow on top end style dan begin mathsize 14px style c with rightwards arrow on top equals stack 4 i with rightwards arrow on top minus j with rightwards arrow on top plus stack 4 k with rightwards arrow on top end style, proyeksi orthogonal vektor begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style open parentheses b with rightwards arrow on top minus c with rightwards harpoon with barb upwards on top close parentheses end style adalah ...

  1. begin mathsize 14px style stack negative 5 i with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top end style 

  2. begin mathsize 14px style stack negative 4 i with rightwards arrow on top plus stack 4 j with rightwards arrow on top minus stack 2 k with rightwards arrow on top end style 

  3. begin mathsize 14px style stack 2 i with rightwards arrow on top minus stack 2 j with rightwards arrow on top plus k with rightwards arrow on top end style 

  4. begin mathsize 14px style stack 4 i with rightwards arrow on top minus stack 4 j with rightwards arrow on top plus stack 2 k with rightwards arrow on top end style 

  5. begin mathsize 14px style stack 6 i with rightwards arrow on top minus stack 6 j with rightwards arrow on top plus stack 3 k with rightwards arrow on top end style 

Pembahasan Video:

Pembahasan:

Proyeksi ortogonal adalah gambar proyeksi yang bidang proyeksinya mempunyai sudut tegak lurus terhadap proyektornya.

Diketahui:

begin mathsize 14px style a with rightwards arrow on top equals stack negative 4 i with rightwards arrow on top plus stack 3 j with rightwards arrow on top minus stack 4 k with rightwards arrow on top b with rightwards arrow on top equals stack negative i with rightwards arrow on top plus j with rightwards arrow on top plus stack 3 k with rightwards arrow on top c with rightwards arrow on top equals stack 4 i with rightwards arrow on top minus j with rightwards arrow on top plus stack 4 k with rightwards arrow on top end style 

 Vektor begin mathsize 14px style open parentheses b with rightwards arrow on top minus c with rightwards harpoon with barb upwards on top close parentheses end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses b with rightwards arrow on top minus c with rightwards arrow on top close parentheses end cell equals cell stack negative i with rightwards arrow on top plus j with rightwards arrow on top plus stack 3 k with rightwards arrow on top minus open parentheses stack 4 i with rightwards arrow on top minus j with rightwards arrow on top plus stack 4 k with rightwards arrow on top close parentheses end cell row blank equals cell stack negative 5 i with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top end cell end table end style 

Proyeksi orthogonal vektor begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style open parentheses b with rightwards arrow on top minus c with rightwards harpoon with barb upwards on top close parentheses end style adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell proyeksi space vektor end cell equals cell open parentheses fraction numerator a with rightwards arrow on top times open parentheses b with rightwards arrow on top minus c with rightwards arrow on top close parentheses over denominator open vertical bar stack b with rightwards arrow on top minus c with rightwards arrow on top with rightwards arrow on top close vertical bar squared end fraction close parentheses open parentheses b with rightwards arrow on top minus c with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses fraction numerator negative 4 left parenthesis negative 5 right parenthesis plus 3 left parenthesis 2 right parenthesis plus left parenthesis negative 4 right parenthesis left parenthesis negative 1 right parenthesis over denominator open parentheses square root of left parenthesis negative 5 right parenthesis squared plus 2 squared plus left parenthesis negative 1 right parenthesis squared end root close parentheses squared end fraction close parentheses open parentheses stack negative 5 j with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses fraction numerator 20 plus 6 plus 4 over denominator open parentheses square root of 25 plus 4 plus 1 end root close parentheses squared end fraction close parentheses open parentheses stack negative 5 j with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 30 over 30 close parentheses open parentheses stack negative 5 j with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top close parentheses end cell row blank equals cell stack negative 5 j with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top end cell end table end style 

Sehingga, proyeksi orthogonal vektor begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style open parentheses b with rightwards arrow on top minus c with rightwards harpoon with barb upwards on top close parentheses end style adalah begin mathsize 14px style stack negative 5 i with rightwards arrow on top plus stack 2 j with rightwards arrow on top minus k with rightwards arrow on top end style.

Jadi, jawaban yang tepat adalah A.

 

Jawaban terverifikasi

Dijawab oleh:

Terakhir diupdate 06 Oktober 2021

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