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For any vector a, then the value of (axxhati)^(2)+(a xxhatj)^(2)+(axxhatk)^(2) is |
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Answer» `4a^(2)` SINCE, `(a xx hati) . (a xx hati) = |{:(a.a,a.hati),(hati.a,1):}| = |a|^(2) - a_(1)^(2)` Similarly , `(axxhatj)^(2) =|a|^(2) - a_2^(2)` and `(a xx hatk)^(2) = |a|^(2) -a_(3)^(2)` `:. (a xx hati)+ (a xx hatj)^(2) + (a xx hatk)^(2) = 3|a|^(2) - (a_(1)^(2)+ a_(2)^(2) + a_(3)^(2))` `= 3|a|^(2) - |a|^(2)` `= 2|a|^(2) = 2a^(2)` |
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