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Bpr621 Bpr621
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Show that A = au + bv is orthogonal to B = bu - av, where u and v are orthogonal unit vectors.
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Calculus: Early Transcendentals


Edition: 3rd
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PurpleBPurpleB
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More questions for this book are available here
AB = (au + bv)∙(bu - av) = abuu - a2uv + b2uv - abvv  = ab - ab = 0
Since the dot product is zero and since neither A nor B is identically zero, A and B are orthogonal.

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