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Diketahui vektor a = ⎝ ⎛ ​ − 4 2 − 2 ​ ⎠ ⎞ ​ dan vektor b = ⎝ ⎛ ​ − 3 3 0 ​ ⎠ ⎞ ​ , tentukan: b. Proyeksi skalar ortogonal a pada b

Diketahui vektor  dan vektor , tentukan:

b. Proyeksi skalar ortogonal  pada  

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E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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proyeksi skalar ortogonal pada adalah .

proyeksi skalar ortogonal a with rightwards arrow on top pada b with rightwards arrow on top adalah square root of 18.

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Pembahasan

Diketahui: Proyeksi skalar ortogonal pada : Jadi, proyeksi skalar ortogonal pada adalah .

Diketahui:

 a with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 2 row cell negative 2 end cell end table close parentheses
b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses

Proyeksi skalar ortogonal a with rightwards arrow on top pada b with rightwards arrow on top open parentheses open vertical bar c with rightwards arrow on top close vertical bar close parentheses:

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 blank equals cell fraction numerator open parentheses table row cell negative 4 end cell row 2 row cell negative 2 end cell end table close parentheses times open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses over denominator square root of open parentheses negative 3 close parentheses squared plus 3 squared plus 0 squared end root end fraction end cell row blank equals cell fraction numerator 12 plus 6 plus 0 over denominator square root of 9 plus 9 plus 0 end root end fraction end cell row blank equals cell fraction numerator 18 over denominator square root of 18 end fraction cross times fraction numerator square root of 18 over denominator square root of 18 end fraction end cell row blank equals cell fraction numerator 18 square root of 18 over denominator 18 end fraction end cell row blank equals cell square root of 18 end cell end table 

Jadi, proyeksi skalar ortogonal a with rightwards arrow on top pada b with rightwards arrow on top adalah square root of 18.

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