A) \[|a{{|}^{2}}b\]
B) \[|a|b\]
C) \[|a{{|}^{3}}b\]
D) \[|a{{|}^{4}}b\]
E) 0
Correct Answer: D
Solution :
Given \[a\bot b\] \[\Rightarrow \] \[a.b=0\] \[=a\times \{a\times \{a\times (a\times b)\}\}\}\] \[=a\times \{a\times \{(a.ba-(a.a)b\}\}\] \[=a\times \{a\times \{0-(a.a)b\}\}\] \[=a\times \{-(a.a)(a\times b)\}\] \[=a\times \{(a.a)(b\times a)\}\] \[=(a.a)\{(a.a)b-(a-b)a\}\] \[=(a.a)\{(a.a)b-0\}\] \[={{(a.a)}^{2}}b\] \[(\because (a.a)=|a{{|}^{2}})\] \[={{(|a{{|}^{2}})}^{2}}b\] \[=|a{{|}^{4}}b\]
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