(Orthonormal bases) Let u D 3 5 i C 4 5 j, v D 4 5 i ? 3 5 j
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(Orthonormal bases) Let u D 3 5 i C 4 5 j, v D 4 5 i ? 3 5 j, and w D k. (a) Show that jujDjvjDjwj D 1 and u v D u w D v
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(Orthonormal bases) Let u D 3 5 i C 4 5 j, v D 4 5 i ? 3 5 j, and w D k. (a) Show that jujDjvjDjwj D 1 and u v D u w D v w D 0. The vectors u, v, and w are mutually perpendicular unit vectors and as such are said to constitute an orthonormal basis for R3 . (b) If r D xi C yj C zk, show by direct calculation thatr D .r u/u C .r v/v C .r w/w:
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