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Pertanyaan

Diketahui vektor a with bar on top equals 2 i minus 5 j dan b with bar on top equals negative 3 i plus 4 j. Tentukan panjang proyeksi ortogonal vektor a with bar on top pada b with bar on top.

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

panjang proyeksi ortogonal vektor a with rightwards arrow on top pada b with rightwards arrow on top adalah open vertical bar c with rightwards arrow on top close vertical bar equals 5 1 fifth.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah bold 5 bold 1 over bold 5.

Panjang proyeksi vektor ortogonal dari vektor a with rightwards arrow on top ke vektor b with rightwards arrow on top ditentukan oleh rumus berikut.

open vertical bar c with rightwards arrow on top close vertical bar equals open vertical bar 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 close vertical bar

Diketahui vektor a with rightwards arrow on top equals 2 i minus 5 j dan b with rightwards arrow on top equals negative 3 i plus 4 j.

Panjang proyeksi ortogonal vektor a with rightwards arrow on top pada b with rightwards arrow on top 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 open vertical bar 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 close vertical bar end cell row blank equals cell open vertical bar fraction numerator 2 times open parentheses negative 3 close parentheses plus open parentheses negative 5 close parentheses times 4 over denominator square root of open parentheses negative 3 close parentheses squared plus 4 squared end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator open parentheses negative 6 close parentheses plus open parentheses negative 20 close parentheses over denominator square root of 25 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 26 over denominator 5 end fraction close vertical bar end cell row blank equals cell 26 over 5 end cell row blank equals cell 5 1 fifth end cell end table

Dengan demikian, panjang proyeksi ortogonal vektor a with rightwards arrow on top pada b with rightwards arrow on top adalah open vertical bar c with rightwards arrow on top close vertical bar equals 5 1 fifth.

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Diketahui vektor p​=i−2j dan q​=−2i+5j. Tentukan proyeksi ortogonal vektor p​ pada q​.

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Jawaban terverifikasi

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