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Q. $ \hat{i}\times (\hat{j}\times \hat{k})+\hat{j}\times (\hat{k}\times \hat{i})+\hat{k}(\hat{i}\times \hat{j}) $ is equal to

Rajasthan PETRajasthan PET 2003

Solution:

$ \hat{i}\times (\hat{j}\times \hat{k})+\hat{j}\times (\hat{k}\times \hat{i})+\hat{k}\times (\hat{i}\times \hat{j}) $
$ =\hat{i}\times \hat{i}+\hat{j}\times \hat{j}+\hat{k}\times \hat{k} $
$ =0+0+0=0 $ $ [\because \hat{i}\times \hat{i}=\hat{j}\times \hat{j}=\hat{k}\times \hat{k}=0] $