Diketahui vektor u = (5,-2) dan v = (4, -2) Proyeksi ortogonal vektor u pada v adalah....
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Jawab:
[tex]\bar w = \frac{1}{5}[16,8] = [\frac{16}{5}, \frac{8}{5}][/tex]
Penjelasan dengan langkah-langkah:
[tex]Dik:\\\bar u = [5,-2]\\\bar v = [4,2]\\\\Dit: \bar w?\ (\bar w\ adalah\ proyeksi\ vektor\ \bar u\ pada\ \bar v)\\\\Jawab:\\\bar w = (\frac{\bar u . \bar v}{|\bar v|^{2}})\bar v\\\\\bar w = (\frac{[5,-2].[4,2]}{(\sqrt{(4)^{2} + (2)^{2}})^{2}})\bar v\\\\\bar w = (\frac{(5)(4) + (-2)(2)}{(4)^{2} + (2)^{2}})\bar v\\\\\bar w = (\frac{20 - 4}{16 + 4})\bar v\\\\\bar w = (\frac{16}{20})\bar v\\\\\bar w = (\frac{4}{5})[4,2] = [\frac{16}{5}, \frac{8}{5}][/tex]
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