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Question

Show that vectors |b|a+|a|band|b|a|a|b are orthogonal.

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Solution

x=ba+|a|b

y=ba|a|b

x and y are orthogonal if their dot product xy=0

(ba+|a|b)(ba|a|b)=

b2aa|a|bab+|a|bab|a|2bb

=b2|a|2|a|2b2

=0

So, x and y are orthogonal

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